Solve for x x^2+x^2=8^2

$x^{2} + x^{2} = 8^{2}$

Step 1

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

$2 x^{2} = 8^{2}$

Step 2

Raise $8$ to the power of $2$ .

$2 x^{2} = 64$

Step 3

Divide each term in $2 x^{2} = 64$ by $2$ and simplify.

Divide each term in $2 x^{2} = 64$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{64}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{64}{2}$

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

$x^{2} = \frac{64}{2}$

Simplify the right side.

Divide $64$ by $2$ .

$x^{2} = 32$

Step 4

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

$x = \pm \sqrt{32}$

Step 5

Simplify $\pm \sqrt{32}$ .

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$x = \pm \sqrt{16 (2)}$

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 4 \sqrt{2}$

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.

$x = 4 \sqrt{2}$

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

$x = - 4 \sqrt{2}$

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

$x = 4 \sqrt{2}, - 4 \sqrt{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt{2}, - 4 \sqrt{2}$

Decimal Form:

$x = 5.65685424 \dots, - 5.65685424 \dots$

Solve for x x^2+x^2=8^2

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