Solve for A A^2+8^2=12^2

$A^{2} + 8^{2} = 12^{2}$

Raise $8$ to the power of $2$ .

$A^{2} + 64 = 12^{2}$

Raise $12$ to the power of $2$ .

$A^{2} + 64 = 144$

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

Subtract $64$ from both sides of the equation.

$A^{2} = 144 - 64$

Subtract $64$ from $144$ .

$A^{2} = 80$

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

$A = \pm \sqrt{80}$

Simplify $\pm \sqrt{80}$ .

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$A = \pm \sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$A = \pm \sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$A = \pm 4 \sqrt{5}$

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.

$A = 4 \sqrt{5}$

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

$A = - 4 \sqrt{5}$

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

$A = 4 \sqrt{5}, - 4 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$A = 4 \sqrt{5}, - 4 \sqrt{5}$

Decimal Form:

$A = 8.94427190 \dots, - 8.94427190 \dots$