Solve for x x^2+1^2=3^2

$x^{2} + 1^{2} = 3^{2}$

Step 1

One to any power is one.

$x^{2} + 1 = 3^{2}$

Step 2

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

$x^{2} + 1 = 9$

Step 3

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$x^{2} = 9 - 1$

Subtract $1$ from $9$ .

$x^{2} = 8$

Step 4

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

$x = \pm \sqrt{8}$

Step 5

Simplify $\pm \sqrt{8}$ .

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.

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

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.

$x = 2 \sqrt{2}$

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.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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