# How do you solve using the completing the square method  x^2 - 4x + 4 = 100?

Sep 5, 2017

$x = 12 , \text{ or } - 8$

#### Explanation:

${x}^{2} - 4 x + 4 = 100$

$\implies {x}^{2} + 4 x = 100 - 4 = 96$

${x}^{2} - 4 x = 96$

take the coefficient of $x$ half it , square it and add and subtract to $L H S$

${x}^{2} - 4 x + {\left(2\right)}^{2} - {\left(2\right)}^{2} = 96$

$\textcolor{red}{{x}^{2} - 4 x + {\left(2\right)}^{2}} - {\left(2\right)}^{2} = 96$

the terms in red forma perfect square

$\textcolor{red}{{\left(x - 2\right)}^{2}} - 4 = 96$

now solve for $x$

${\left(x - 2\right)}^{2} = 96 + 4 = 100$

$x - 2 = \pm \sqrt{100}$

$x - 2 = \pm 10$

$: x = + 10 + 2 , \text{or } x = - 10 + 2$

$\therefore x = 12 , \text{ or } - 8$