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

Jul 15, 2017

See a solution process below:

Explanation:

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

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

$\sqrt{x - 2} + 0 = 1$

$\sqrt{x - 2} = 1$

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

${\left(\sqrt{x - 2}\right)}^{2} = {1}^{2}$

$x - 2 = 1$

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

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

$x - 0 = 3$

$x = 3$