# How do you solve  ( x + 5)² = 49?

Jun 1, 2016

$x = - 12$ or $x = 2$

#### Explanation:

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

or ${\left(x + 5\right)}^{2} - 49 = 0$

or ${\left(x + 5\right)}^{2} - {7}^{2} = 0$

Now using a^2-b^2=(a+b_(a-b)

The above is equivalent to $\left(\left(x + 5\right) + 7\right) \left(\left(x + 5\right) - 7\right) = 0$

or $\left(x + 12\right) \left(x - 2\right) = 0$

Hence either $x + 12 = 0$ or $x - 2 = 0$

i.e. $x = - 12$ or $x = 2$