Question

Solve:$\sqrt{3m+2}-5=0$

Short answer

The solution is$m=\frac{23}{3}$.

Step-by-step solution

Step 1. Given Information  

We are given the quadratic equation $\sqrt{3m+2}-5=0$and we need to solve it.

Step 2. Finding the solution 

Isolating the radical on one side of the equation:

$$\begin{gathered} \sqrt{3m+2}-5=0 \\ \Rightarrow \sqrt{3m+2}-5+5=5 \\ \Rightarrow \sqrt{3m+2}=5 \end{gathered}$$

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{3m+2}\right)}^2={\left(5\right)}^2 \\ \Rightarrow 3m+2=25 \\ \Rightarrow 3m=25-2 \\ \Rightarrow 3m=23 \\ \Rightarrow m=\frac{23}{3} \end{gathered}$$

Step 3. Checking the answer 

$$\begin{gathered} m=\frac{23}{3}, \\ \sqrt{3\left(\frac{23}{3}\right)+2}-5=0 \\ \Rightarrow \sqrt{23+2}-5=0 \\ \Rightarrow \sqrt{25}-5=0 \\ \Rightarrow 5-5=0 \\ \Rightarrow 0=0 \end{gathered}$$