Algebra Examples

${(x - 5)}^{2} = 7$

Step 1

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

$x - 5 = \pm \sqrt{7}$

Step 2

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

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Step 2.1

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

$x - 5 = \sqrt{7}$

Step 2.2

Add $5$ to both sides of the equation.

$x = \sqrt{7} + 5$

Step 2.3

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

$x - 5 = - \sqrt{7}$

Step 2.4

Add $5$ to both sides of the equation.

$x = - \sqrt{7} + 5$

Step 2.5

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

$x = \sqrt{7} + 5, - \sqrt{7} + 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7} + 5, - \sqrt{7} + 5$

Decimal Form:

$x = 7.64575131 \dots, 2.35424868 \dots$