Pre-Algebra Examples

${(x + 10)}^{2} + y^{2} = 4$

Step 1

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

${(x + 10)}^{2} = 4 - y^{2}$

Step 2

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

$x + 10 = \pm \sqrt{4 - y^{2}}$

Step 3

Simplify $\pm \sqrt{4 - y^{2}}$ .

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Step 3.1

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

$x + 10 = \pm \sqrt{2^{2} - y^{2}}$

Step 3.2

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

$x + 10 = \pm \sqrt{(2 + y) (2 - y)}$

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.

$x + 10 = \sqrt{(2 + y) (2 - y)}$

Step 4.2

Subtract $10$ from both sides of the equation.

$x = \sqrt{(2 + y) (2 - y)} - 10$

Step 4.3

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

$x + 10 = - \sqrt{(2 + y) (2 - y)}$

Step 4.4

Subtract $10$ from both sides of the equation.

$x = - \sqrt{(2 + y) (2 - y)} - 10$

Step 4.5

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

$x = \sqrt{(2 + y) (2 - y)} - 10$

$x = - \sqrt{(2 + y) (2 - y)} - 10$

$x = \sqrt{(2 + y) (2 - y)} - 10$

$x = - \sqrt{(2 + y) (2 - y)} - 10$