How do you solve sqrt(8x)+1=65 and check the solution?

May 23, 2017

See a solution process below:

Explanation:

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

$\sqrt{8 x} + 1 - \textcolor{red}{1} = 65 - \textcolor{red}{1}$

$\sqrt{8 x} + 0 = 64$

$\sqrt{8 x} = 64$

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

${\left(\sqrt{8 x}\right)}^{2} = {64}^{2}$

$8 x = 4096$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $x$ while keeping the equation balanced:

$\frac{8 x}{\textcolor{red}{8}} = \frac{4096}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} x}{\cancel{\textcolor{red}{8}}} = 512$

$x = 512$

To check the solution substitute $\textcolor{red}{512}$ for $\textcolor{red}{x}$ and calculate each side of the equation to ensure both sides are equal:

$\sqrt{8 \textcolor{red}{x}} + 1 = 65$ becomes:

$\sqrt{8 \cdot \textcolor{red}{512}} + 1 = 65$

$\sqrt{4096} + 1 = 65$

$64 + 1 = 65$

$65 + 65$

Both sides of the equation are equal therefore the solution is valid.