Question

Other Equations Find all real solutions of the equation.

$\sqrt{8x-1}=3$

Short answer

The real solution of the given equation is $x=1.25$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\sqrt{8x-1}=3$

Step 3. Solve the given equation.

Squaring both sides, the given equation can be rewritten as:

$$\begin{gathered} {\left(\sqrt{8x-1}\right)}^2={\left(3\right)}^2 \\ 8x-1=9 \end{gathered}$$

Add$1$ on both sides.

$$\begin{gathered} 8x-1+1=9+1 \\ 8x=10 \end{gathered}$$

Divide both sides by $8$.

$$\begin{gathered} \frac{8x}{8}=\frac{10}{8} \\ x=\frac{5}{4} \\ x=1.25 \end{gathered}$$

Thus, the real solution of the given equation is $x=1.25$.