Basic Math Examples

${(a + 6)}^{2} + {(y + 2)}^{2} = 64$

Step 1

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

${(a + 6)}^{2} = 64 - {(y + 2)}^{2}$

Step 2

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

$a + 6 = \pm \sqrt{64 - {(y + 2)}^{2}}$

Step 3

Simplify $\pm \sqrt{64 - {(y + 2)}^{2}}$ .

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Step 3.1

Rewrite $64$ as $8^{2}$ .

$a + 6 = \pm \sqrt{8^{2} - {(y + 2)}^{2}}$

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 $a = 8$ and $b = y + 2$ .

$a + 6 = \pm \sqrt{(8 + y + 2) (8 - (y + 2))}$

Step 3.3

Simplify.

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Step 3.3.1

Add $8$ and $2$ .

$a + 6 = \pm \sqrt{(y + 10) (8 - (y + 2))}$

Step 3.3.2

Apply the distributive property.

$a + 6 = \pm \sqrt{(y + 10) (8 - y - 1 \cdot 2)}$

Step 3.3.3

Multiply $- 1$ by $2$ .

$a + 6 = \pm \sqrt{(y + 10) (8 - y - 2)}$

Step 3.3.4

Subtract $2$ from $8$ .

$a + 6 = \pm \sqrt{(y + 10) (- y + 6)}$

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.

$a + 6 = \sqrt{(y + 10) (- y + 6)}$

Step 4.2

Subtract $6$ from both sides of the equation.

$a = \sqrt{(y + 10) (- y + 6)} - 6$

Step 4.3

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

$a + 6 = - \sqrt{(y + 10) (- y + 6)}$

Step 4.4

Subtract $6$ from both sides of the equation.

$a = - \sqrt{(y + 10) (- y + 6)} - 6$

Step 4.5

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

$a = \sqrt{(y + 10) (- y + 6)} - 6$

$a = - \sqrt{(y + 10) (- y + 6)} - 6$

$a = \sqrt{(y + 10) (- y + 6)} - 6$

$a = - \sqrt{(y + 10) (- y + 6)} - 6$