Q. 17 - Intermediate Algebra

Question

In the following exercises, solve each equation.

$\frac{2}{5}{a}^2+3=11$

Step-by-Step Solution

Answer

The solution of the equation is $a=2\sqrt{5},-2\sqrt{5}$

Step 1. Given information

In the given question we have to solve given equation.
$\frac{2}{5}{a}^2+3=11$

Step 2. The given equation is 2 5 a 2 + 3 = 11

Isolate the quadratic term.

Subtract 3 on both side

$$\begin{gathered} \frac{2}{5}{a}^2+3-3=11-3 \\ \frac{2}{5}{a}^2=8 \end{gathered}$$

Multiply by $\frac{5}{2}$on both side

$$\begin{gathered} \frac{2}{5}{a}^2\times \frac{5}{2}=8\times \frac{5}{2} \\ {a}^2=4\times 5 \end{gathered}$$

Step 3. Use the Square Root Property.

$a=\pm \sqrt{4\times 5}$

Simplify the radical.

$a=\pm 2\sqrt{5}$

Step 4. Rewrite to show two solutions.

$a=2\sqrt{5} a=-2\sqrt{5}$