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

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

Rewrite the equation as $x^{2} = 2^{2} + 2^{2}$ .

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

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

$x^{2} = 2 \cdot 2^{2}$

Multiply $2$ by $2^{2}$ by adding the exponents.

Multiply $2$ by $2^{2}$ .

Raise $2$ to the power of $1$ .

$x^{2} = 2^{1} \cdot 2^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} = 2^{1 + 2}$

Add $1$ and $2$ .

$x^{2} = 2^{3}$

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

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

Simplify $\pm \sqrt{2^{3}}$ .

Raise $2$ to the power of $3$ .

$x = \pm \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

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.

$x = 2 \sqrt{2}$

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

$x = - 2 \sqrt{2}$

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.82842712 \dots, - 2.82842712 \dots$