Solve for x 1^2+x^2=5^2

$1^{2} + x^{2} = 5^{2}$

Step 1

One to any power is one.

$1 + x^{2} = 5^{2}$

Step 2

Raise $5$ to the power of $2$ .

$1 + x^{2} = 25$

Step 3

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

Subtract $1$ from both sides of the equation.

$x^{2} = 25 - 1$

Subtract $1$ from $25$ .

$x^{2} = 24$

Step 4

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

$x = \pm \sqrt{24}$

Step 5

Simplify $\pm \sqrt{24}$ .

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \pm \sqrt{4 (6)}$

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

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

Pull terms out from under the radical.

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

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.

$x = 2 \sqrt{6}$

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

$x = - 2 \sqrt{6}$

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.89897948 \dots, - 4.89897948 \dots$