Solve for x (x-5)^2+5=49

${(x - 5)}^{2} + 5 = 49$

Step 1

Subtract $5$ from both sides of the equation.

${(x - 5)}^{2} = 49 - 5$

Step 2

Subtract $5$ from $49$ .

${(x - 5)}^{2} = 44$

Step 3

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

$x - 5 = \pm \sqrt{44}$

Step 4

Simplify $\pm \sqrt{44}$ .

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x - 5 = \pm \sqrt{4 (11)}$

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

$x - 5 = \pm \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$x - 5 = \pm 2 \sqrt{11}$

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.

$x - 5 = 2 \sqrt{11}$

Add $5$ to both sides of the equation.

$x = 2 \sqrt{11} + 5$

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

$x - 5 = - 2 \sqrt{11}$

Add $5$ to both sides of the equation.

$x = - 2 \sqrt{11} + 5$

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

$x = 2 \sqrt{11} + 5, - 2 \sqrt{11} + 5$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{11} + 5, - 2 \sqrt{11} + 5$

Decimal Form:

$x = 11.63324958 \dots, - 1.63324958 \dots$