Question

Solve: $\sqrt{3x-5}=5$.

Short answer

The solution is$x=10$.

Step-by-step solution

Step 1. Given Information    

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

Step 2. Finding the solution

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{3x-5}\right)}^2={\left(5\right)}^2 \\ \Rightarrow 3x-5=25 \\ \Rightarrow 3x=25+5 \\ \Rightarrow 3x=30 \\ \Rightarrow x=\frac{30}{3} \\ \Rightarrow x=10 \end{gathered}$$

Step 3. Checking the answer

$$\begin{gathered} x=10, \\ \sqrt{3\times 10-5}=5 \\ \Rightarrow \sqrt{30-5}=5 \\ \Rightarrow \sqrt{25}=5 \\ \Rightarrow 5=5 \end{gathered}$$