# How do you solve (x - 8)^2 = 48?

Jul 24, 2017

See a solution process below:

#### Explanation:

First, take the square root of each side of the equation to eliminate the exponent while keeping the equation balanced. Remember, the square root of a number gives both a positive and a negative result:

$\sqrt{{\left(x - 8\right)}^{2}} = \pm \sqrt{48}$

$x - 8 = + \sqrt{48}$ and $x - 8 = - \sqrt{48}$

$x - 8 = \sqrt{16 \cdot 3}$ and $x - 8 = - \sqrt{16 \cdot 3}$

$x - 8 = \sqrt{16} \cdot \sqrt{3}$ and $x - 8 = - \sqrt{16} \sqrt{3}$

$x - 8 = 4 \sqrt{3}$ and $x - 8 = - 4 \sqrt{3}$

$x - 8 + \textcolor{red}{8} = 4 \sqrt{3} + \textcolor{red}{8}$ and $x - 8 + \textcolor{red}{8} = - 4 \sqrt{3} + \textcolor{red}{8}$

$x - 0 = 4 \sqrt{3} + 8$ and $x - 0 = - 4 \sqrt{3} + 8$

$x = 4 \sqrt{3} + 8$ and $x = - 4 \sqrt{3} + 8$