Q. 30 - Intermediate Algebra

Question

In the following exercises, solve each equation.

${\left(t-\frac{5}{6}\right)}^2=\frac{11}{25}$

Step-by-Step Solution

Answer

The solution of the equation is $t=\frac{5}{6}+\frac{\sqrt{11}}{5},\frac{5}{6}-\frac{\sqrt{11}}{5}$

Step 1. Given information

In the given question we have to solve given equation.

${\left(t-\frac{5}{6}\right)}^2=\frac{11}{25}$

Step 2. The given equation is t − 5 6 2 = 11 25

Use the Square Root Property.

$$\begin{gathered} t-\frac{5}{6}=\pm \sqrt{\frac{11}{25}} \\ t-\frac{5}{6}=\pm \frac{\sqrt{11}}{\sqrt{25}} \end{gathered}$$

Step 3. Simplify the radical.

$t-\frac{5}{6}=\pm \frac{\sqrt{11}}{5}$

Add $\frac{5}{6}$on both side

$$\begin{gathered} t-\frac{5}{6}+\frac{5}{6}=\frac{5}{6}\pm \frac{\sqrt{11}}{5} \\ t=\frac{5}{6}\pm \frac{\sqrt{11}}{5} \end{gathered}$$

Step 4. Solve for t

$t=\frac{5}{6}+\frac{\sqrt{11}}{5} t=\frac{5}{6}-\frac{\sqrt{11}}{5}$