Pre-Algebra Examples

${(2 x - 6)}^{2} = 23$

Step 1

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

$2 x - 6 = \pm \sqrt{23}$

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.

$2 x - 6 = \sqrt{23}$

Step 2.2

Add $6$ to both sides of the equation.

$2 x = \sqrt{23} + 6$

Step 2.3

Divide each term in $2 x = \sqrt{23} + 6$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 x = \sqrt{23} + 6$ by $2$ .

$\frac{2 x}{2} = \frac{\sqrt{23}}{2} + \frac{6}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{\sqrt{23}}{2} + \frac{6}{2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{23}}{2} + \frac{6}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $6$ by $2$ .

$x = \frac{\sqrt{23}}{2} + 3$

Step 2.4

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

$2 x - 6 = - \sqrt{23}$

Step 2.5

Add $6$ to both sides of the equation.

$2 x = - \sqrt{23} + 6$

Step 2.6

Divide each term in $2 x = - \sqrt{23} + 6$ by $2$ and simplify.

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Step 2.6.1

Divide each term in $2 x = - \sqrt{23} + 6$ by $2$ .

$\frac{2 x}{2} = \frac{- \sqrt{23}}{2} + \frac{6}{2}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $2$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \sqrt{23}}{2} + \frac{6}{2}$

Step 2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{23}}{2} + \frac{6}{2}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Simplify each term.

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Step 2.6.3.1.1

Move the negative in front of the fraction.

$x = - \frac{\sqrt{23}}{2} + \frac{6}{2}$

Step 2.6.3.1.2

Divide $6$ by $2$ .

$x = - \frac{\sqrt{23}}{2} + 3$

Step 2.7

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

$x = \frac{\sqrt{23}}{2} + 3, - \frac{\sqrt{23}}{2} + 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{23}}{2} + 3, - \frac{\sqrt{23}}{2} + 3$

Decimal Form:

$x = 5.39791576 \dots, 0.60208423 \dots$