Basic Math Examples

${(s + a)}^{2} + {(y + b)}^{2} = r^{2}$

Step 1

Subtract ${(s + a)}^{2}$ from both sides of the equation.

${(y + b)}^{2} = r^{2} - {(s + a)}^{2}$

Step 2

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

$y + b = \pm \sqrt{r^{2} - {(s + a)}^{2}}$

Step 3

Simplify $\pm \sqrt{r^{2} - {(s + a)}^{2}}$ .

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Step 3.1

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

$y + b = \pm \sqrt{(r + s + a) (r - (s + a))}$

Step 3.2

Apply the distributive property.

$y + b = \pm \sqrt{(r + s + a) (r - s - a)}$

Step 4

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

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Step 4.1

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

$y + b = \sqrt{(r + s + a) (r - s - a)}$

Step 4.2

Subtract $b$ from both sides of the equation.

$y = \sqrt{(r + s + a) (r - s - a)} - b$

Step 4.3

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

$y + b = - \sqrt{(r + s + a) (r - s - a)}$

Step 4.4

Subtract $b$ from both sides of the equation.

$y = - \sqrt{(r + s + a) (r - s - a)} - b$

Step 4.5

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

$y = \sqrt{(r + s + a) (r - s - a)} - b$

$y = - \sqrt{(r + s + a) (r - s - a)} - b$

$y = \sqrt{(r + s + a) (r - s - a)} - b$

$y = - \sqrt{(r + s + a) (r - s - a)} - b$