# How do you solve 5=sqrtx+1 and check your solution?

Jul 27, 2017

See a solution process below:

#### Explanation:

Solution:

First, subtract $\textcolor{red}{1}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$5 - \textcolor{red}{1} = \sqrt{x} + 1 - \textcolor{red}{1}$

$4 = \sqrt{x} + 0$

$4 = \sqrt{x}$

Now, square both sides of the equation to solve for $x$ while keeping the equation balanced:

${4}^{\textcolor{red}{2}} = {\left(\sqrt{x}\right)}^{\textcolor{red}{2}}$

$16 = x$

$x = 16$

Check Solution:

Substitute $\textcolor{red}{16}$ into the original solution for $\textcolor{red}{x}$ and calculate both sides of the equation to ensure they are equal:

$5 = \sqrt{\textcolor{red}{x}} + 1$ becomes:

$5 = \sqrt{\textcolor{red}{16}} + 1$

Remember, the square root of a number produces both a positive and negative solution:

$5 = 4 + 1$ and $5 = - 4 + 1$

$5 = 5$ and $5 = - 3$

The check on the left shows our solution is correct.

The check on the right is an extraneous solution and can be ignored.