Question

Solve:$\sqrt{5q+1}+4=6$.

Short answer

The solution is$q=\frac{3}{5}$.

Step-by-step solution

Step 1. Given Information 

We are given the quadratic equation $\sqrt{5q+1}+4=6$and we need to solve it.

Step 2. Finding the solution   

Isolating the radical on one side of the equation:

$$\begin{gathered} \sqrt{5q+1}+4=6 \\ \Rightarrow \sqrt{5q+1}+4-4=6-4 \\ \Rightarrow \sqrt{5q+1}=2 \end{gathered}$$

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{5q+1}\right)}^2={\left(2\right)}^2 \\ \Rightarrow 5q+1=4 \\ \Rightarrow 5q=4-1 \\ \Rightarrow 5q=3 \\ \Rightarrow q=\frac{3}{5} \end{gathered}$$

Step 3. Checking the answer  

$$\begin{gathered} q=\frac{3}{5}, \\ \sqrt{5q+1}+4=6 \\ \Rightarrow \sqrt{5\times \frac{3}{5}+1}+4=6 \\ \Rightarrow \sqrt{3+1}+4=6 \\ \Rightarrow \sqrt{4}+4=6 \\ \Rightarrow 2+4=6 \\ \Rightarrow 6=6 \end{gathered}$$