<Text-field style="Heading 1" layout="Heading 1">Motiva\303\247\303\243o</Text-field>

Fun\303\247\303\243o do Segundo Grau:

Completando o Quadrado

O gr\303\241fico da quadr\303\241tica 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 \303\251 uma par\303\241bola com o eixo de simetria paralelo ao eixo vertical. O v\303\251rtice ser\303\241 o ponto mais alto no gr\303\241fico (se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8) ou o mais baixo (se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8). Localizando o v\303\251rtice \303\251 muito mais simples se a par\303\241bola estiver escrita na sua forma v\303\251rtice.

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

onde 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 e 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 s\303\243o uma conseq\303\274\303\252ncia do processo de completar o quadrado. O v\303\251rtice \303\251 o ponto

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

Al\303\251m disso, os zeros de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= agora s\303\243o f\303\241ceis de determinar:

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

Esta \303\251 a f\303\263rmula quadr\303\241tica, a f\303\263rmula para os zeros da fun\303\247\303\243o quadr\303\241tica 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.

<Text-field style="Heading 1" layout="Heading 1">O Que Significa Completar o Quadrado ?</Text-field>

A equa\303\247\303\243o para um polin\303\264mio quadr\303\241tico pode ser escrito em forma de v\303\251rtice 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 ou na forma mais geral 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. Para reescrever o primeiro para o segundo \303\251 f\303\241cil, basta multiplicar a express\303\243o e simplificar. Indo no sentido inverso \303\251 mais dif\303\255cil. Isso \303\251 o que esta t\303\251cnica faz: reescreve um polin\303\264mio quadr\303\241tico de uma forma geral, sob a forma de v\303\251rtice.

Considere o polin\303\264mio quadr\303\241tico

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. \303\211 evidente que esta polinomial quadr\303\241tica \303\251 um quadrado perfeito, desde 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. Mas e sobre o quadr\303\241tico 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? O n\303\272mero 10 n\303\243o \303\251 o quadrado de 3 e, portanto, este polin\303\264mio n\303\243o \303\251 um quadrado perfeito. No entanto, \303\251 poss\303\255vel expressar o polin\303\264mio usando um quadrado por escrito

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JJW1zdXBHRiQ2JS1GLDYmUSJ4RidGL0YyRjUtRiM2JS1JI21uR0YkNiVRIjJGJ0YyRjxGMkY8LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GOTYuUSIrRidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjIyMjIyMmVtRicvRlBGXm8tRlo2JVEiNkYnRjJGPC1GOTYuUScmc2RvdDtGJ0YyRjxGPkZARkJGREZGRkhGSi9GTVEmMC4wZW1GJy9GUEZnb0ZULUY5Ni9GXG8vJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRidGMkY8Rj5GQEZCRkRGRkZIRkpGXW9GX28tRlo2JlEiOUYnRltwRjJGPEZpby1GWjYmUSIxRidGW3BGMkY8RjJGPA==

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

Este \303\251 um exemplo do processo chamado "completando o quadrado."

Quadrados-perfeitos assumem a forma:

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

Quadr\303\241ticas que n\303\243o s\303\243o quadrados perfeitos, tomam a forma de um parte quadrada mais uma constante:

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

<Text-field style="Heading 1" layout="Heading 1">Como Completar o Quadrado?</Text-field>

JSFH

Primeiro, considere um exemplo simples com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjkvRj1RJ25vcm1hbEYnLyUmZmVuY2VHRjsvJSpzZXBhcmF0b3JHRjsvJSlzdHJldGNoeUdGOy8lKnN5bW1ldHJpY0dGOy8lKGxhcmdlb3BHRjsvJS5tb3ZhYmxlbGltaXRzR0Y7LyUnYWNjZW50R0Y7LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVS1JI21uR0YkNiVRIjFGJ0Y5RkNGOUZDRitGOUZDRitGOUZD.

Complete o quadrado: 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

Passos

Descri\303\247\303\243o

Solu\303\247\303\243o

(1)

Divida o coeficiente do termo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn por 2 e eleve ao quadrado este quociente.

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

(2)

Na express\303\243o quadr\303\241tica, adcionar e subtrair esta quantidade

(Isso n\303\243o mudou a equa\303\247\303\243o.)

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

(3)

Agrupe os termos do quadrado-perfeito juntos.

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

(4)

Adicione os valores constantes em conjunto e escreva a quadr\303\241tica como um quadrado perfeito mais uma constante.

Portanto, a fun\303\247\303\243o 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, escrito como quadrado perfeito, \303\251 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.

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Em seguida, considere um exemplo com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlErJk5vdEVxdWFsO0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjFGJ0YyRjxGMkY8.

Complete o quadrado: 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

Passos

Descri\303\247\303\243o

Solu\303\247\303\243o

(1)

Se h\303\241 um fator em comum entre os termos que cont\303\251m x, fator\303\241-lo.

Aqui, factore o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JI21uR0YkNiVRIjJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y1RjhGK0Y1Rjg=.

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

(2)

Divida o coeficiente do termo-x por 2, e eleve ao quadrado este quociente.

(3)

Dentro dos par\303\252nteses, somar e subtrair esta quantidade.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1JI21vR0YkNi5RIj1GJ0YyRkAvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWLUkjbW5HRiQ2JVEiMkYnRjJGQC1GQzYuUScmc2RvdDtGJ0YyRkBGRkZIRkpGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZbby1GOTYlLUYjNi4tRkM2LlEifkYnRjJGQEZGRkhGSkZMRk5GUEZSRmpuRlxvLUklbXN1cEdGJDYlRj0tRiM2JUZZRjJGQC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRkM2LlEiK0YnRjJGQEZGRkhGSkZMRk5GUEZSL0ZVUSwwLjIyMjIyMjJlbUYnL0ZYRmBwLUZaNiVRIjZGJ0YyRkBGZ25GPS1GQzYvRl5wLyUrZm9yZWdyb3VuZEdRKlswLDAsMjU1XUYnRjJGQEZGRkhGSkZMRk5GUEZSRl9wRmFwLUZaNiZRIjlGJ0ZncEYyRkAtRkM2L1EoJm1pbnVzO0YnRmdwRjJGQEZGRkhGSkZMRk5GUEZSRl9wRmFwRmpwRjJGQEYyRkBGXHAtRlo2JVEjMTdGJ0YyRkBGMkZA

(4)

A quadr\303\241tica agora \303\251 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. para remover o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiYtSSNtb0dGJDYuUSomdW1pbnVzMDtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0Y5LyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk0tSSNtbkdGJDYlUSI5RidGN0Y6RjdGOkYrRjdGOkYrRjdGOg== a partir do par\303\252nteses, multiplic\303\241-lo por 2, tornando-se -18.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQC1JI21vR0YkNi5RIj1GJ0YyRkAvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWLUkjbW5HRiQ2JVEiMkYnRjJGQC1GQzYuUScmc2RvdDtGJ0YyRkBGRkZIRkpGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZbby1GOTYlLUYjNistSSVtc3VwR0YkNiVGPS1GIzYmRllGL0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZDNi5RIitGJ0YyRkBGRkZIRkpGTEZORlBGUi9GVVEsMC4yMjIyMjIyZW1GJy9GWEZdcC1GWjYlUSI2RidGMkZARmduRj1GaW8tRlo2JVEiOUYnRjJGQEYyRkBGMkZARmlvLUZaNiVRIzE3RidGMkZALUZDNi5RKCZtaW51cztGJ0YyRkBGRkZIRkpGTEZORlBGUkZccEZecC1GWjYlUSMxOEYnRjJGQEYyRkA=

(5)

Adicione os valores constantes em conjunto e escrever o quadrado perfeito como um termo ao quadrado.

A equa\303\247\303\243o 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, escrito como um quadrado completo, \303\251

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.

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

Resumo das Etapas para Completar o Quadrado:

Agrupar os termos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYyRjw= juntos (fator comum, se poss\303\255vel).

Eleve ao quadrado a metade do coeficiente do termo em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn. Adicione e subtrair estes valores..

Mova a constante extra para fora dos par\303\252nteses. Se houve um fator comum, lembre-se multiplic\303\241-lo por esse n\303\272mero.

Escreva os tr\303\252s termos do quadrado perfeito como um quadrado.

Combinar os valores constantes.

E voila!

Nota: \303\211 f\303\241cil de verificar o seu trabalho. Basta expandir a sua resposta final e garantir que voc\303\252 volte a equa\303\247\303\243o original.

<Text-field style="Heading 1" layout="Heading 1">Demonstra\303\247\303\243o</Text-field>

Use esta demonstra\303\247\303\243o passo-a-passo para explorar completando o quadrado. Clique no bot\303\243o "Gerar Polin\303\264mios quadr\303\241ticos" para gerar um novo polin\303\264mio quadr\303\241tico, e clique no "Executar este passo" para ver os resultados de cada etapa.

Gerar Polin\303\264mios Quadr\303\241ticos:

use DocumentTools in #Clear Boxes before bringing in the next question seq(SetProperty(i,value,NULL),i in [MathContainer1, MathContainer2, MathContainer3]); _myA, _myB, _myC := op(RandomTools:-Generate([integer(range = -10 .. 10), integer(range = -10 .. 10), integer(range = 1 .. 6)])); if _myA = 0 then _myA := _myB; _myB := 0; end if; _myEq := expand(_myC*(x+_myA)^2+_myB); Do(%MathContainer0=_myEq); end use;

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Equa\303\247\303\243o Original:

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Passo 1:

Agrupar os termos vari\303\241vel.

use DocumentTools in #Update section Do(%MathContainer0=_myEq); _Temp := PolynomialTools[CoefficientList](collect(_myEq, x), x); _TempCF := _Temp[3]; _Temp[2] := _Temp[2]/_TempCF; SetProperty(MathContainer1, value, MathML:-ExportPresentation(``*_TempCF*(x^2+_Temp[2]*x)+_Temp[1])); _NextStep:=2; end use;

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Equa\303\247\303\243o ap\303\263s Passo 1:

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Passo 2:

Para completar o quadrado, somar e subtrair o quadrado da metade do termo m\303\251dio.

use DocumentTools in #Update section if _NextStep=2 then _SqIn:=(_Temp[2]/2)^2; SetProperty(MathContainer2, value, MathML:-ExportPresentation(``*_TempCF*(x^2+_Temp[2]*x+_SqIn)+``*_Temp[1]-_SqIn*_TempCF)); _NextStep:=3; end if; end use;

Equa\303\247\303\243o ap\303\263s Passo 2:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Passo 3:

Escreva os tr\303\252s termos dentro dos par\303\252nteses como um quadrado perfeito e simplifique.

use DocumentTools in #Update section if _myEq<>NULL then Do(%MathContainer0=_myEq); if _NextStep=3 then SetProperty(MathContainer3, value, MathML:-ExportPresentation(``*_TempCF*(factor(x^2+_Temp[2]*x+_SqIn))+_Temp[1]-_SqIn*_TempCF)); end if; end if; end use;

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Equa\303\247\303\243o ap\303\263s Passo 3:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

use DocumentTools in seq(SetProperty(i,value,NULL),i in [MathContainer0, MathContainer1, MathContainer2, MathContainer3]); _NextStep:=1; end use;

use DocumentTools in seq(SetProperty(i,value,NULL),i in [MathContainer0, MathContainer1, MathContainer2, MathContainer3]); _myEq:=NULL; end use;

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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