Q. 15 - Intermediate Algebra

Question

In the following exercises, solve each equation.

$\frac{4}{3}{x}^2+2=110$

Step-by-Step Solution

Answer

The solution of the equation is $x=9,-9$

Step 1. Given information

In the given question we have to solve given equation.
$\frac{4}{3}{x}^2+2=110$

Step 2. The given equation is 4 3 x 2 + 2 = 110

Isolate the quadratic term.

Subtract 2 on both side

$$\begin{gathered} \frac{4}{3}{x}^2+2-2=110-2 \\ \frac{4}{3}{x}^2=108 \end{gathered}$$

Multiply by $\frac{3}{4}$ on both side

$$\begin{gathered} \frac{4}{3}{x}^2\times \frac{3}{4}=108\times \frac{3}{4} \\ {x}^2=27\times 3 \\ {x}^2=81 \end{gathered}$$

Step 3. Use the Square Root Property.

$x=\pm \sqrt{81}$

Simplify the radical.

$x=\pm 9$

Step 4. Rewrite to show two solutions.

$x=9 x=-9$