Q. 28 - Intermediate Algebra

Question

In the following exercises, solve each equation.

${\left(x+\frac{1}{5}\right)}^2=\frac{7}{25}$

Step-by-Step Solution

Answer

The solution of the equation is $x=\frac{-1+\sqrt{7}}{5},\frac{-1-\sqrt{7}}{5}$

Step 1. Given information

In the given question we have to solve given equation. 

${\left(x+\frac{1}{5}\right)}^2=\frac{7}{25}$

Step 2. The given equation is x + 1 5 2 = 7 25

Use the Square Root Property.

$x+\frac{1}{5}=\pm \sqrt{\frac{7}{25}}$

Step 3. Simplify the radical.

$$\begin{gathered} x+\frac{1}{5}=\pm \frac{\sqrt{7}}{\sqrt{25}} \\ x+\frac{1}{5}=\pm \frac{\sqrt{7}}{5} \end{gathered}$$

Subtract $\frac{1}{5}$on both side

$$\begin{gathered} x+\frac{1}{5}-\frac{1}{5}=-\frac{1}{5}\pm \frac{\sqrt{7}}{5} \\ x=-\frac{1}{5}\pm \frac{\sqrt{7}}{5} \end{gathered}$$

Step 4. Solve for x

$$\begin{gathered} x=-\frac{1}{5}+\frac{\sqrt{7}}{5} x=-\frac{1}{5}-\frac{\sqrt{7}}{5} \\ x=\frac{-1+\sqrt{7}}{5} x=\frac{-1-\sqrt{7}}{5} \end{gathered}$$