# How do you solve -5sqrt(8x-4) +3 = 18?

Oct 20, 2015

$x \in \emptyset$

#### Explanation:

The idea when dealing with radical equations is to start by isolating the radical term on one side of the equation.

In your case, you can do that by adding $- 3$ to both sides of the equation and dividing all the terms by $- 5$.

$- 5 \sqrt{8 x - 4} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} = 18 - 3$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} \sqrt{8 x - 4}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(- 5\right)}}}} = \frac{15}{\left(- 5\right)}$

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

Notice that you have the square root returning a negative value. This cannot happen when dealing with real numbers because you can only take the square root of positive numbers and you will always get a positive number as a result.

This means that the original equation has no real solutions, or $x \in \emptyset$.