Solve for x x^2+x^2=6^2

$x^{2} + x^{2} = 6^{2}$

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} = 6^{2}$

Raise $6$ to the power of $2$ .

$2 x^{2} = 36$

Divide each term in $2 x^{2} = 36$ by $2$ and simplify.

Divide each term in $2 x^{2} = 36$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{36}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{36}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{36}{2}$

Simplify the right side.

Divide $36$ by $2$ .

$x^{2} = 18$

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

$x = \pm \sqrt{18}$

Simplify $\pm \sqrt{18}$ .

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$x = \pm \sqrt{9 (2)}$

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

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

Pull terms out from under the radical.

$x = \pm 3 \sqrt{2}$

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.

$x = 3 \sqrt{2}$

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

$x = - 3 \sqrt{2}$

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

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{2}, - 3 \sqrt{2}$

Decimal Form:

$x = 4.24264068 \dots, - 4.24264068 \dots$