Finite Math Examples

${(s + 5)}^{2} + 18 = 0$

Step 1

Subtract $18$ from both sides of the equation.

${(s + 5)}^{2} = - 18$

Step 2

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

$s + 5 = \pm \sqrt{- 18}$

Step 3

Simplify $\pm \sqrt{- 18}$ .

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Step 3.1

Rewrite $- 18$ as $- 1 (18)$ .

$s + 5 = \pm \sqrt{- 1 (18)}$

Step 3.2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$s + 5 = \pm \sqrt{- 1} \cdot \sqrt{18}$

Step 3.3

Rewrite $\sqrt{- 1}$ as $i$ .

$s + 5 = \pm i \cdot \sqrt{18}$

Step 3.4

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 3.4.1

Factor $9$ out of $18$ .

$s + 5 = \pm i \cdot \sqrt{9 (2)}$

Step 3.4.2

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

$s + 5 = \pm i \cdot \sqrt{3^{2} \cdot 2}$

Step 3.5

Pull terms out from under the radical.

$s + 5 = \pm i \cdot (3 \sqrt{2})$

Step 3.6

Move $3$ to the left of $i$ .

$s + 5 = \pm 3 i \sqrt{2}$

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.

$s + 5 = 3 i \sqrt{2}$

Step 4.2

Subtract $5$ from both sides of the equation.

$s = 3 i \sqrt{2} - 5$

Step 4.3

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

$s + 5 = - 3 i \sqrt{2}$

Step 4.4

Subtract $5$ from both sides of the equation.

$s = - 3 i \sqrt{2} - 5$

Step 4.5

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

$s = 3 i \sqrt{2} - 5, - 3 i \sqrt{2} - 5$