Precalculus Examples

$| 3 x - 2 | = 2 \sqrt{x + 8}$

Step 1

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 \sqrt{x + 8} = | 3 x - 2 |$

Step 2

Rewrite the equation as $| 3 x - 2 | = 2 \sqrt{x + 8}$ .

$| 3 x - 2 | = 2 \sqrt{x + 8}$

Step 3

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 x - 2 = \pm 2 \sqrt{x + 8}$

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.

$3 x - 2 = 2 \sqrt{x + 8}$

Step 4.2

Add $2$ to both sides of the equation.

$3 x = 2 \sqrt{x + 8} + 2$

Step 4.3

Divide each term in $3 x = 2 \sqrt{x + 8} + 2$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 x = 2 \sqrt{x + 8} + 2$ by $3$ .

$\frac{3 x}{3} = \frac{2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.4

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

$3 x - 2 = - 2 \sqrt{x + 8}$

Step 4.5

Add $2$ to both sides of the equation.

$3 x = - 2 \sqrt{x + 8} + 2$

Step 4.6

Divide each term in $3 x = - 2 \sqrt{x + 8} + 2$ by $3$ and simplify.

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Step 4.6.1

Divide each term in $3 x = - 2 \sqrt{x + 8} + 2$ by $3$ .

$\frac{3 x}{3} = \frac{- 2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $3$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Move the negative in front of the fraction.

$x = - \frac{2 \sqrt{x + 8}}{3} + \frac{2}{3}$

Step 4.7

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

$x =$