Solve for b a^2=b^2+c^2

$a^{2} = b^{2} + c^{2}$

Step 1

Rewrite the equation as $b^{2} + c^{2} = a^{2}$ .

$b^{2} + c^{2} = a^{2}$

Step 2

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

$b^{2} = a^{2} - c^{2}$

Step 3

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

$b = \pm \sqrt{a^{2} - c^{2}}$

Step 4

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

$b = \pm \sqrt{(a + c) (a - c)}$

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.

$b = \sqrt{(a + c) (a - c)}$

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

$b = - \sqrt{(a + c) (a - c)}$

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

$b = \sqrt{(a + c) (a - c)}$

$b = - \sqrt{(a + c) (a - c)}$

$b = \sqrt{(a + c) (a - c)}$

$b = - \sqrt{(a + c) (a - c)}$