# How do you solve a^2 - 10a +18 = 0 by completing the square?

Jan 15, 2017

$a = 5 \pm \sqrt{7}$

#### Explanation:

Since ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$, we need the middle term to be

$- 2 a b$, so we use $5$ as $b$.

${a}^{2} - 10 a + 25 = {\left(a - 5\right)}^{2}$, so ${\left(a - 5\right)}^{2} - 7 = 0 \implies {\left(a - 5\right)}^{2} = 7$

$a - 5 = \pm \sqrt{7} \implies a = 5 \pm \sqrt{7}$