Finite Math Examples

${(3 y + 18)}^{2} = 48$

Step 1

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

$3 y + 18 = \pm \sqrt{48}$

Step 2

Simplify $\pm \sqrt{48}$ .

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Step 2.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 2.1.1

Factor $16$ out of $48$ .

$3 y + 18 = \pm \sqrt{16 (3)}$

Step 2.1.2

Rewrite $16$ as $4^{2}$ .

$3 y + 18 = \pm \sqrt{4^{2} \cdot 3}$

Step 2.2

Pull terms out from under the radical.

$3 y + 18 = \pm 4 \sqrt{3}$

Step 3

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

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$3 y + 18 = 4 \sqrt{3}$

Step 3.2

Subtract $18$ from both sides of the equation.

$3 y = 4 \sqrt{3} - 18$

Step 3.3

Divide each term in $3 y = 4 \sqrt{3} - 18$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $3 y = 4 \sqrt{3} - 18$ by $3$ .

$\frac{3 y}{3} = \frac{4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 18$ by $3$ .

$y = \frac{4 \sqrt{3}}{3} - 6$

Step 3.4

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

$3 y + 18 = - 4 \sqrt{3}$

Step 3.5

Subtract $18$ from both sides of the equation.

$3 y = - 4 \sqrt{3} - 18$

Step 3.6

Divide each term in $3 y = - 4 \sqrt{3} - 18$ by $3$ and simplify.

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Step 3.6.1

Divide each term in $3 y = - 4 \sqrt{3} - 18$ by $3$ .

$\frac{3 y}{3} = \frac{- 4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $3$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Simplify each term.

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Step 3.6.3.1.1

Move the negative in front of the fraction.

$y = - \frac{4 \sqrt{3}}{3} + \frac{- 18}{3}$

Step 3.6.3.1.2

Divide $- 18$ by $3$ .

$y = - \frac{4 \sqrt{3}}{3} - 6$

Step 3.7

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

$y = \frac{4 \sqrt{3}}{3} - 6, - \frac{4 \sqrt{3}}{3} - 6$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4 \sqrt{3}}{3} - 6, - \frac{4 \sqrt{3}}{3} - 6$

Decimal Form:

$y = - 3.69059892 \dots, - 8.30940107 \dots$