# How do you solve sqrt(2x+5) +6=4?

Aug 11, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{6}$ from each side of the equation to isolate the radical while keeping the equation balanced:

$\sqrt{2 x + 5} + 6 - \textcolor{red}{6} = 4 - \textcolor{red}{6}$

$\sqrt{2 x + 5} + 0 = - 2$

$\sqrt{2 x + 5} = - 2$

Next, square each side of the equation to eliminate the radical while keeping the equation balanced:

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

2x + 5 = 4#

Now, subtract $\textcolor{red}{5}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$2 x + 5 - \textcolor{red}{5} = 4 - \textcolor{red}{5}$

$2 x + 0 = - 1$

$2 x = - 1$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$\frac{2 x}{\textcolor{red}{2}} = - \frac{1}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} = - \frac{1}{2}$

$x = - \frac{1}{2}$

To check the answer we can substitute $- \frac{1}{2}$ for $x$ and calculate the result:

$\sqrt{2 x + 5} + 6 = 4$ becomes:

$\sqrt{\left(2 \times - \frac{1}{2}\right) + 5} + 6 = 4$

$\sqrt{- 1 + 5} + 6 = 4$

$\sqrt{4} + 6 = 4$

Remember, the square root of a number produces both a positive AND negative result:

$- 2 + 6 = 4$ and $2 + 6 = 4$

$4 = 4$ and $8 \ne 4$

The solution for $\sqrt{4} = 2$ is an extraneous solution.

The solution for $\sqrt{4} = - 2$ is a valid solution.