Question

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

Answer 1

Answer:

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,

$x=13,\:x=3$