Calculus Examples

$9^{2} + y^{2} = 225$

Step 1

Raise $9$ to the power of $2$ .

$81 + y^{2} = 225$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Subtract $81$ from both sides of the equation.

$y^{2} = 225 - 81$

Step 2.2

Subtract $81$ from $225$ .

$y^{2} = 144$

Step 3

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

$y = \pm \sqrt{144}$

Step 4

Simplify $\pm \sqrt{144}$ .

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Step 4.1

Rewrite $144$ as $12^{2}$ .

$y = \pm \sqrt{12^{2}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 12$

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.

$y = 12$

Step 5.2

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

$y = - 12$

Step 5.3

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

$y = 12, - 12$