# How do you solve x^2-24x=10 by completing the square?

Oct 22, 2017

#### Answer:

$x = 24.4097 , - 0.4097$

#### Explanation:

${x}^{2} - 24 x = 10$

${x}^{2} + \left(2 \left(x\right) \left(- 12\right)\right) = 10$

${x}^{2} + \left(2 \left(x\right) \left(- 12\right)\right) + 144 - 144 = 10$ (Add and subtract 144)

 x^2 + ( 2 (x)(-12) + (12)^2 = 154#
${\left(x - 12\right)}^{2} = 154$
$\left(x - 12\right) = \pm \sqrt{154} \textcolor{w h i t e}{a a a}$taking square root on both sides
$x = 12 \pm \sqrt{154}$
$x = 24.4097 , - 0.4097$

Oct 22, 2017

#### Answer:

$x = 12 \pm \sqrt{154}$

#### Explanation:

Completing the square means making the ${x}^{2}$ and $x$ terms take the form ${x}^{2} + 2 n x + {n}^{2}$. Where in this case $n = - 12$.

So, ${x}^{2} - 24 x = 10$ becomes ${x}^{2} - 24 x + 144 = 10 + 144$.
So, ${\left(x - 12\right)}^{2} = 154$
$x = 12 \pm \sqrt{154}$