Mathematics: 20 Points!!Complete The Square formula for:x2 -16x + 39 = 0

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20 Points!!Complete The Square formula for:x2 -16x

Ответ:

cschellfamily

18.03.2022

Mathematics

Please check the explanation.

Step-by-step explanation:

Given the equation

$x^2\:-16x\:+\:39\:=\:0$

Subtract 39 from both sides

x^2-16x+39-39=0-39

Simplify

x^2-16x=-39

Rewrite in the form x² + 2ax + a²

solve for a, 2ax = -16x

2ax = -16x

divide both sides by 2a

2ax/2x = -16x/2x

a = -8

Add a² = (-8)² to both sides

$x^2-16x+\left(-8\right)^2=-39+\left(-8\right)^2$

simplify

$x^2-16x+\left(-8\right)^2=25$

Apply perfect square formula: (a-b)² = a² - 2ab + b²

$\left(x-8\right)^2=25$ ∵ $x^2-16x+\left(-8\right)^2=\left(x-8\right)^2$

Thus,

$\left(x-8\right)^2=25$

BONUS! EXTENDED SOLUTION!

We can further solve for x such as

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solve

$x-8=\sqrt{25}$

$x-8=\sqrt{5^2}$

x-8=5

x=13

similarly,

$x-8=-\sqrt{25}$

x-8=-5

x=3

Therefore,

$x=13,\:x=3$

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20 Points!!

Complete The Square formula for:
x2 -16x + 39 = 0

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