Answer
$x=4$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given eqution, $
x^2-8x+16=0
,$ express the equation in factored form. Then, use the Square Root Principle to solve the resulting equation.
$\bf{\text{Solution Details:}}$
In the trinomial expression above, the value of $c$ is $
16
$ and the value of $b$ is $
-8
.$
The possible pairs of integers whose product is $c$ are
\begin{array}{l}\require{cancel}
\{ 1,16 \}, \{ 2,8 \}, \{ 4,4 \},
\\
\{ -1,-16 \}, \{ -2,-8 \}, \{ -4,-4 \}
.\end{array}
Among these pairs, the one that gives a sum of $b$ is $\{
-4,-4
\}.$ Hence, the factored form of the equation above is
\begin{array}{l}\require{cancel}
(x-4)(x-4)=0
\\\\
(x-4)^2=0
.\end{array}
Taking the square root of both sides (Square Root Principle), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x-4=\pm\sqrt{0}
\\\\
x-4=0
\\\\
x=4
.\end{array}
