# How do you solve using the completing the square method x^2- 10x = -8?

May 20, 2018

$x = 5 \pm \sqrt{17}$

#### Explanation:

${x}^{2} - 10 x = - 8$

$a {x}^{2} + b x + c$.

To complete the square a =1 and $c = {\left(\frac{1}{2} b\right)}^{2}$

$c = {\left(\frac{1}{2} \cdot - 10\right)}^{2} = 25$, a already is 1

we need to add the c to both sides of the equation so we don't change its value:

${x}^{2} - 10 x + c = - 8 + c$

${x}^{2} - 10 x + 25 = - 8 + 25$

the -5 is the $\frac{1}{2} b$ before we squared it:

${\left(x - 5\right)}^{2} = 17$

$\sqrt{{\left(x - 5\right)}^{2}} = \pm \sqrt{17}$

$x - 5 = \pm \sqrt{17}$

$x = 5 \pm \sqrt{17}$

graph{x^2- 10x +8 [-13.16, 26.84, -18.56, 1.44]}