How do you solve (x-5)^2=49?

May 14, 2016

$x = 12 , - 2$

Explanation:

${\left(x - 5\right)}^{2} = 49$

We know that $49 = {7}^{2} \text{ and } 49 = - {7}^{2}$

Find the square-root of both sides:

$x - 5 = \pm 7$

When $x - 5 = 7$

Add $5$ to both sides:

$x - 5 \textcolor{red}{+ 5} = 7 \textcolor{red}{+ 5}$

$x = 12$

When $x - 5 = - 7$

Add $5$ to both sides:

$x - 5 \textcolor{red}{+ 5} = - 7 \textcolor{red}{+ 5}$

$x = - 2$