Solve for x 4^2=3^2+x^2

$4^{2} = 3^{2} + x^{2}$

Step 1

Rewrite the equation as $3^{2} + x^{2} = 4^{2}$ .

$3^{2} + x^{2} = 4^{2}$

Step 2

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

$9 + x^{2} = 4^{2}$

Step 3

Raise $4$ to the power of $2$ .

$9 + x^{2} = 16$

Step 4

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

Subtract $9$ from both sides of the equation.

$x^{2} = 16 - 9$

Subtract $9$ from $16$ .

$x^{2} = 7$

Step 5

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

$x = \pm \sqrt{7}$

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.

$x = \sqrt{7}$

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

$x = - \sqrt{7}$

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.64575131 \dots, - 2.64575131 \dots$