Evaluate 4r^2-5=59

$4 r^{2} - 5 = 59$

Step 1

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

Add $5$ to both sides of the equation.

$4 r^{2} = 59 + 5$

Add $59$ and $5$ .

$4 r^{2} = 64$

Step 2

Divide each term in $4 r^{2} = 64$ by $4$ and simplify.

Divide each term in $4 r^{2} = 64$ by $4$ .

$\frac{4 r^{2}}{4} = \frac{64}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r^{2}}{4} = \frac{64}{4}$

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

$r^{2} = \frac{64}{4}$

Simplify the right side.

Divide $64$ by $4$ .

$r^{2} = 16$

Step 3

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

$r = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

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

$r = \pm \sqrt{4^{2}}$

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

$r = \pm 4$

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.

$r = 4$

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

$r = - 4$

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

$r = 4, - 4$