# How do you solve by completing the square: x^2=8x+10?

Jul 7, 2018

$x = 4 \pm \sqrt{26}$

#### Explanation:

Given: ${x}^{2} = 8 x + 10$. Solve using completing of the square.

First, group the monomials with $x$ together on the same side:

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

To complete the square, multiply the constant of the $x$ monomial by $\frac{1}{2}$: $\text{ } - 8 \cdot \frac{1}{2} = - \frac{8}{2} = - 4$

When you complete the square you end up adding a square term:
${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

${\left(x - 4\right)}^{2} = {x}^{2} - 8 x + \textcolor{red}{{\left(- 4\right)}^{2}}$

This term must be also added to the right side of the equation:

${\left(x - 4\right)}^{2} = 10 + {\left(- 4\right)}^{2}$

${\left(x - 4\right)}^{2} = 26$

Square root both sides:

$x - 4 = \pm \sqrt{26}$

$x = 4 \pm \sqrt{26}$