# How do you factor and solve X^2 + 100 = 20X?

Oct 2, 2016

$x = 10$

#### Explanation:

${x}^{2} + 100 = 20 x$

${x}^{2} \textcolor{w h i t e}{a a a a a a} + 100 = \textcolor{w h i t e}{a} 20 x$
$\textcolor{w h i t e}{a a} - 20 x \textcolor{w h i t e}{a a a a a a a} - 20 x \textcolor{w h i t e}{a a a}$Subtract $20 x$ from both sides.

${x}^{2} - 20 x + 100 = 0$
$\left(x - 10\right) \left(x - 10\right) = 0 \textcolor{w h i t e}{a a a a a}$Factor

$x - 10 = 0 \textcolor{w h i t e}{a a a} x - 10 = 0 \textcolor{w h i t e}{a a a}$Set each factor equal to zero

$x - 10 = \textcolor{w h i t e}{a a} 0$
$\textcolor{w h i t e}{a} + 10 \textcolor{w h i t e}{a a} + 10 \textcolor{w h i t e}{a a a}$Add 10 to both sides

$x = 10$