Precalculus Examples

$y^{2} = 5^{2} - 4^{2}$

Step 1

Raise $4$ to the power of $2$ .

$y^{2} = 5^{2} - 1 \cdot 16$

Step 2

Multiply $- 1$ by $16$ .

$y^{2} = 5^{2} - 16$

Step 3

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

$y = \pm \sqrt{5^{2} - 16}$

Step 4

Simplify $\pm \sqrt{5^{2} - 16}$ .

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Step 4.1

Raise $5$ to the power of $2$ .

$y = \pm \sqrt{25 - 16}$

Step 4.2

Subtract $16$ from $25$ .

$y = \pm \sqrt{9}$

Step 4.3

Rewrite $9$ as $3^{2}$ .

$y = \pm \sqrt{3^{2}}$

Step 4.4

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

$y = \pm 3$

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.

$y = 3$

Step 5.2

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

$y = - 3$

Step 5.3

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

$y = 3, - 3$