Question

Solve:$\sqrt{10z+1}-2=0$

Short answer

The solution is $z=\frac{3}{10}$.

Step-by-step solution

Step 1. Given Information 

We are given the quadratic equation $\sqrt{10z+1}-2=0$and we need to solve it.

Step 2. Finding the solution  

Isolating the radical on one side of the equation:

$$\begin{gathered} \sqrt{10z+1}-2=0 \\ \Rightarrow \sqrt{10z+1}-2+2=2 \\ \Rightarrow \sqrt{10z+1}=2 \end{gathered}$$

Squaring both sides of the equation, we get:

$$\begin{gathered} {\left(\sqrt{10z+1}\right)}^2={\left(2\right)}^2 \\ \Rightarrow 10z+1=4 \\ \Rightarrow 10z=4-1 \\ \Rightarrow 10z=3 \\ \Rightarrow z=\frac{3}{10} \end{gathered}$$

Step 3. Checking the answer 

$$\begin{gathered} z=\frac{3}{10}, \\ \sqrt{10z+1}-2=0 \\ \Rightarrow \sqrt{10\left(\frac{3}{10}\right)+1}-2=0 \\ \Rightarrow \sqrt{3+1}-2=0 \\ \Rightarrow \sqrt{4}-2=0 \\ \Rightarrow 2-2=0 \\ \Rightarrow 0=0 \end{gathered}$$