Question

In the following exercises, solve using the Square Root Property.

${\left(x-\frac{1}{4}\right)}^2=\frac{3}{16}$

Short answer

The required answer is$x=\frac{\sqrt{3}}{4}+\frac{1}{4}\mathrm{and}x=-\frac{\sqrt{3}}{4}+\frac{1}{4}$.

Step-by-step solution

Step 1. Given information.

The given quadratic equation is:

${\left(x-\frac{1}{4}\right)}^2=\frac{3}{16}$

Step 2. Solve using the quadratic equation by using Square Root Property. 

${\left(x-\frac{1}{4}\right)}^2=\frac{3}{16}$

Use Square Root Property,

$x-\frac{1}{4}=\pm \sqrt{\frac{3}{16}}$

Simplify the radical,

$$\begin{gathered} x-\frac{1}{4}=\pm \frac{\sqrt{3}}{\sqrt{16}} \\ x-\frac{1}{4}=\pm \frac{\sqrt{3}}{4} \end{gathered}$$

Write as two equations and solve,

$$\begin{gathered} x-\frac{1}{4}=\frac{\sqrt{3}}{4}\mathrm{and}x-\frac{1}{4}=-\frac{\sqrt{3}}{4} \\ x=\frac{\sqrt{3}}{4}+\frac{1}{4}\mathrm{and}x=-\frac{\sqrt{3}}{4}+\frac{1}{4} \end{gathered}$$