Solve for x (x-10)^2+10=100

${(x - 10)}^{2} + 10 = 100$

Subtract $10$ from both sides of the equation.

${(x - 10)}^{2} = 100 - 10$

Subtract $10$ from $100$ .

${(x - 10)}^{2} = 90$

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

$x - 10 = \pm \sqrt{90}$

Simplify $\pm \sqrt{90}$ .

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$x - 10 = \pm \sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$x - 10 = \pm \sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$x - 10 = \pm 3 \sqrt{10}$

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.

$x - 10 = 3 \sqrt{10}$

Add $10$ to both sides of the equation.

$x = 3 \sqrt{10} + 10$

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

$x - 10 = - 3 \sqrt{10}$

Add $10$ to both sides of the equation.

$x = - 3 \sqrt{10} + 10$

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

$x = 3 \sqrt{10} + 10, - 3 \sqrt{10} + 10$

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{10} + 10, - 3 \sqrt{10} + 10$

Decimal Form:

$x = 19.48683298 \dots, 0.51316701 \dots$