Q. 22 - Intermediate Algebra

Question

In the following exercises, solve each equation.

$3x^2-8=46$

Step-by-Step Solution

Answer

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

Step 1. Given information

In the given question we have to solve given equation.
$3x^2-8=46$

Step 2. The given equation is 3 x 2 − 8 = 46

Isolate the quadratic term.

Add 8 on both side

$$\begin{gathered} 3x^2-8+8=46+8 \\ 3x^2=54 \end{gathered}$$

Divide by 3 on both side

$\frac{3}{3}{x}^2=\frac{54}{3}$

$x^2=8$

Step 3. Use the Square Root Property.

$x=\pm \sqrt{8}$

Simplify the radical.

$$\begin{gathered} x=\pm \sqrt{2\times 4} \\ x=\pm 2\sqrt{2} \end{gathered}$$

Step 4. Rewrite to show two solutions.

$x=2\sqrt{2} x=-2\sqrt{2}$