Precalculus Examples

${(5 x - 2)}^{2} = 6$

Step 1

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

$5 x - 2 = \pm \sqrt{6}$

Step 2

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

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Step 2.1

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

$5 x - 2 = \sqrt{6}$

Step 2.2

Add $2$ to both sides of the equation.

$5 x = \sqrt{6} + 2$

Step 2.3

Divide each term in $5 x = \sqrt{6} + 2$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = \sqrt{6} + 2$ by $5$ .

$\frac{5 x}{5} = \frac{\sqrt{6}}{5} + \frac{2}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\sqrt{6}}{5} + \frac{2}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{6}}{5} + \frac{2}{5}$

Step 2.4

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

$5 x - 2 = - \sqrt{6}$

Step 2.5

Add $2$ to both sides of the equation.

$5 x = - \sqrt{6} + 2$

Step 2.6

Divide each term in $5 x = - \sqrt{6} + 2$ by $5$ and simplify.

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Step 2.6.1

Divide each term in $5 x = - \sqrt{6} + 2$ by $5$ .

$\frac{5 x}{5} = \frac{- \sqrt{6}}{5} + \frac{2}{5}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $5$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \sqrt{6}}{5} + \frac{2}{5}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{6}}{5} + \frac{2}{5}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Move the negative in front of the fraction.

$x = - \frac{\sqrt{6}}{5} + \frac{2}{5}$

Step 2.7

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

$x = \frac{\sqrt{6}}{5} + \frac{2}{5}, - \frac{\sqrt{6}}{5} + \frac{2}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{6}}{5} + \frac{2}{5}, - \frac{\sqrt{6}}{5} + \frac{2}{5}$

Decimal Form:

$x = 0.88989794 \dots, - 0.08989794 \dots$