# How do you solve 2(7x + 18) − 1 = (x + 6)^2?

Mar 12, 2018

The solution is $x = 1$.

#### Explanation:

Expand the multiplication and then factor the leftover polynomial:

color(red)2(7x + 18) − 1 = (x + 6)^2

$\textcolor{red}{2} \cdot 7 x + \textcolor{red}{2} \cdot 18 - 1 = {\left(x + 6\right)}^{2}$

$14 x + 36 - 1 = {\left(x + 6\right)}^{2}$

$14 x + 35 = \left(x + 6\right) \left(x + 6\right)$

$14 x + 35 = {x}^{2} + 6 x + 6 x + 36$

$14 x + 35 = {x}^{2} + 12 x + 36$

$35 = {x}^{2} - 2 x + 36$

$0 = {x}^{2} - 2 x + 1$

$0 = {\left(x - 1\right)}^{2}$

$\sqrt{0} = \sqrt{{\left(x - 1\right)}^{2}}$

$0 = x - 1$

$x = 1$