Solve for x 7^2+7^2=x^2

$7^{2} + 7^{2} = x^{2}$

Rewrite the equation as $x^{2} = 7^{2} + 7^{2}$ .

$x^{2} = 7^{2} + 7^{2}$

Add $7^{2}$ and $7^{2}$ .

$x^{2} = 2 \cdot 7^{2}$

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

$x = \pm \sqrt{2 \cdot 7^{2}}$

Simplify $\pm \sqrt{2 \cdot 7^{2}}$ .

Raise $7$ to the power of $2$ .

$x = \pm \sqrt{2 \cdot 49}$

Multiply $2$ by $49$ .

$x = \pm \sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$x = \pm \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 7 \sqrt{2}$

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.

$x = 7 \sqrt{2}$

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

$x = - 7 \sqrt{2}$

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

$x = 7 \sqrt{2}, - 7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$x = 7 \sqrt{2}, - 7 \sqrt{2}$

Decimal Form:

$x = 9.89949493 \dots, - 9.89949493 \dots$