Solve for x x^2+x^2=12^2

$x^{2} + x^{2} = 12^{2}$

Step 1

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

$2 x^{2} = 12^{2}$

Step 2

Raise $12$ to the power of $2$ .

$2 x^{2} = 144$

Step 3

Divide each term in $2 x^{2} = 144$ by $2$ and simplify.

Divide each term in $2 x^{2} = 144$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{144}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{144}{2}$

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

$x^{2} = \frac{144}{2}$

Simplify the right side.

Divide $144$ by $2$ .

$x^{2} = 72$

Step 4

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

$x = \pm \sqrt{72}$

Step 5

Simplify $\pm \sqrt{72}$ .

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \pm \sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 6 \sqrt{2}$

Step 6

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.

$x = 6 \sqrt{2}$

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

$x = - 6 \sqrt{2}$

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

$x = 6 \sqrt{2}, - 6 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 6 \sqrt{2}, - 6 \sqrt{2}$

Decimal Form:

$x = 8.48528137 \dots, - 8.48528137 \dots$

Solve for x x^2+x^2=12^2

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