Solve for x 4(x^2-8)=84

$4 (x^{2} - 8) = 84$

Divide each term in $4 (x^{2} - 8) = 84$ by $4$ and simplify.

Divide each term in $4 (x^{2} - 8) = 84$ by $4$ .

$\frac{4 (x^{2} - 8)}{4} = \frac{84}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (x^{2} - 8)}{4} = \frac{84}{4}$

Divide $x^{2} - 8$ by $1$ .

$x^{2} - 8 = \frac{84}{4}$

Simplify the right side.

Divide $84$ by $4$ .

$x^{2} - 8 = 21$

Move all terms not containing $x$ to the right side of the equation.

Add $8$ to both sides of the equation.

$x^{2} = 21 + 8$

Add $21$ and $8$ .

$x^{2} = 29$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{29}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{29}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{29}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{29}, - \sqrt{29}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{29}, - \sqrt{29}$

Decimal Form:

$x = 5.38516480 \dots, - 5.38516480 \dots$