Question

Solve:$\sqrt{4x+8}=6$.

Short answer

The solution is $x=7$.

Step-by-step solution

Step 1. Given Information  

We are given the quadratic equation $\sqrt{4x+8}=6$and we need to solve it.

Step 2. Finding the solution 

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{4x+8}\right)}^2={\left(6\right)}^2 \\ \Rightarrow 4x+8=36 \\ \Rightarrow 4x=36-8 \\ \Rightarrow 4x=28 \\ \Rightarrow x=\frac{28}{4} \\ \Rightarrow x=7 \end{gathered}$$

Step 3. Checking the answer 

$$\begin{gathered} x=7, \\ \sqrt{4x+8}=6 \\ \Rightarrow \sqrt{4\times 7+8}=6 \\ \Rightarrow \sqrt{28+8}=6 \\ \Rightarrow \sqrt{36}=6 \\ \Rightarrow 6=6 \end{gathered}$$