Pre-Algebra Examples

${(r + 6)}^{2} = 15$

Step 1

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

$r + 6 = \pm \sqrt{15}$

Step 2

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

Tap for more steps...

Step 2.1

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

$r + 6 = \sqrt{15}$

Step 2.2

Subtract $6$ from both sides of the equation.

$r = \sqrt{15} - 6$

Step 2.3

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

$r + 6 = - \sqrt{15}$

Step 2.4

Subtract $6$ from both sides of the equation.

$r = - \sqrt{15} - 6$

Step 2.5

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

$r = \sqrt{15} - 6, - \sqrt{15} - 6$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = \sqrt{15} - 6, - \sqrt{15} - 6$

Decimal Form:

$r = - 2.12701665 \dots, - 9.87298334 \dots$