Q. 21 - Intermediate Algebra

Question

In the following exercises, solve each equation.

$5y^2-7=25$

Step-by-Step Solution

Answer

The solution of the equation is $y=4\sqrt{\frac{2}{5}},-4\sqrt{\frac{2}{5}}$

Step 1. Given information

In the given question we have to solve given equation.
$5y^2-7=25$

Step 2. The given equation is 5 y 2 − 7 = 25

Isolate the quadratic term.

Add 7 on both side

$$\begin{gathered} 5y^2-7+7=25+7 \\ 5y^2=32 \end{gathered}$$

Divide by 5 on both side

$$\begin{gathered} \frac{5}{5}{y}^2=\frac{32}{5} \\ {y}^2=\frac{32}{5} \end{gathered}$$

Step 3. Use the Square Root Property.

$y=\pm \sqrt{\frac{32}{5}}$

Simplify the radical.

$$\begin{gathered} y=\pm \sqrt{\frac{16\times 2}{5}} \\ y=\pm 4\sqrt{\frac{2}{5}} \end{gathered}$$

Step 4. Rewrite to show two solutions.

$y=4\sqrt{\frac{2}{5}} y=-4\sqrt{\frac{2}{5}}$