Solve Using the Square Root Property x^2-4=76

$x^{2} - 4 = 76$

Step 1

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

Add $4$ to both sides of the equation.

$x^{2} = 76 + 4$

Add $76$ and $4$ .

$x^{2} = 80$

Step 2

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

$x = \pm \sqrt{80}$

Step 3

Simplify $\pm \sqrt{80}$ .

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$x = \pm \sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$x = \pm 4 \sqrt{5}$

Step 4

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.

$x = 4 \sqrt{5}$

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

$x = - 4 \sqrt{5}$

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

$x = 4 \sqrt{5}, - 4 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{5}, - 4 \sqrt{5}$

Decimal Form:

$x = 8.94427190 \dots, - 8.94427190 \dots$