# How do you solve 2(a-6)^2-45=53?

Aug 18, 2016

$a = - 1 \mathmr{and} a = 13$

#### Explanation:

This is a quadratic equation which we can solve by an easy method because there is no term in $a$.

$2 {\left(a - 6\right)}^{2} - 45 = 53 \text{ isolate the term with the variable}$

$2 {\left(a - 6\right)}^{2} = 53 + 45$

$2 {\left(a - 6\right)}^{2} = 98 \text{ isolate the factor with the variable}$

${\left(a - 6\right)}^{2} = 49 \text{ find the square root of both sides}$

$a - 6 = \pm 7$

$a - 6 = + 7 \Rightarrow a = 7 + 6 = 13$
$a - 6 = - 7 \Rightarrow a = - 7 + 6 = - 1$