# How do you solve  5x^2 – 100x + 455 = 0  by completing the square?

Jun 30, 2015

$x = 7$
or
$x = 13$

#### Explanation:

$5 {x}^{2} - 100 x + 455 = 0$

First simplify by dividing both sides by 5
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} - 20 x + 91 = 0$

If $\left({x}^{2} - 20 x\right)$ are the first two terms of a spared binomial the third term must be $\left(+ 100\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$since ${\left(x - a\right)}^{2} = {x}^{2} - 2 a x + {a}^{2}$

Completing the square
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} - 20 x + 100 - 9 = 0$

$\textcolor{w h i t e}{\text{XXXX}}$${\left(x - 10\right)}^{2} = 9$

Taking the square root of both sides
$\textcolor{w h i t e}{\text{XXXX}}$$x - 10 = \pm \sqrt{9} = \pm 3$

$\textcolor{w h i t e}{\text{XXXX}}$x=7$\mathmr{and}$x=13#