Solve by Factoring A^2+B^2=C^2

$A^{2} + B^{2} = C^{2}$

Step 1

Subtract $C^{2}$ from both sides of the equation.

$A^{2} + B^{2} - C^{2} = 0$

Step 2

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

Subtract $B^{2}$ from both sides of the equation.

$A^{2} - C^{2} = - B^{2}$

Add $C^{2}$ to both sides of the equation.

$A^{2} = - B^{2} + C^{2}$

Step 3

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

$A = \pm \sqrt{- B^{2} + C^{2}}$

Step 4

Simplify $\pm \sqrt{- B^{2} + C^{2}}$ .

Reorder $- B^{2}$ and $C^{2}$ .

$A = \pm \sqrt{C^{2} - B^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = C$ and $b = B$ .

$A = \pm \sqrt{(C + B) (C - B)}$

Step 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.

$A = \sqrt{(C + B) (C - B)}$

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

$A = - \sqrt{(C + B) (C - B)}$

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

$A = \sqrt{(C + B) (C - B)}$

$A = - \sqrt{(C + B) (C - B)}$

$A = \sqrt{(C + B) (C - B)}$

$A = - \sqrt{(C + B) (C - B)}$