Basic Math Examples

$a^{2} + 72^{2} = c^{2}$

Step 1

Raise $72$ to the power of $2$ .

$a^{2} + 5184 = c^{2}$

Step 2

Subtract $5184$ from both sides of the equation.

$a^{2} = c^{2} - 5184$

Step 3

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

$a = \pm \sqrt{c^{2} - 5184}$

Step 4

Simplify $\pm \sqrt{c^{2} - 5184}$ .

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Step 4.1

Rewrite $5184$ as $72^{2}$ .

$a = \pm \sqrt{c^{2} - 72^{2}}$

Step 4.2

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 $b = 72$ .

$a = \pm \sqrt{(c + 72) (c - 72)}$

Step 5

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

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

$a = \sqrt{(c + 72) (c - 72)}$

Step 5.2

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

$a = - \sqrt{(c + 72) (c - 72)}$

Step 5.3

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

$a = \sqrt{(c + 72) (c - 72)}$

$a = - \sqrt{(c + 72) (c - 72)}$

$a = \sqrt{(c + 72) (c - 72)}$

$a = - \sqrt{(c + 72) (c - 72)}$