Solve for x (x-9)^2+26=31

${(x - 9)}^{2} + 26 = 31$

Subtract $26$ from both sides of the equation.

${(x - 9)}^{2} = 31 - 26$

Subtract $26$ from $31$ .

${(x - 9)}^{2} = 5$

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

$x - 9 = \pm \sqrt{5}$

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.

$x - 9 = \sqrt{5}$

Add $9$ to both sides of the equation.

$x = \sqrt{5} + 9$

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

$x - 9 = - \sqrt{5}$

Add $9$ to both sides of the equation.

$x = - \sqrt{5} + 9$

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

$x = \sqrt{5} + 9, - \sqrt{5} + 9$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5} + 9, - \sqrt{5} + 9$

Decimal Form:

$x = 11.23606797 \dots, 6.76393202 \dots$