Solve Using the Square Root Property 4x^2+65=81

$4 x^{2} + 65 = 81$

Step 1

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

Subtract $65$ from both sides of the equation.

$4 x^{2} = 81 - 65$

Subtract $65$ from $81$ .

$4 x^{2} = 16$

Step 2

Divide each term in $4 x^{2} = 16$ by $4$ and simplify.

Divide each term in $4 x^{2} = 16$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{16}{4}$

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

$x^{2} = \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$x^{2} = 4$

Step 3

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

$x = \pm \sqrt{4}$

Step 4

Simplify $\pm \sqrt{4}$ .

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

$x = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 2$

Step 5

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$