Solve Using the Square Root Property (2x-6)^2=21

${(2 x - 6)}^{2} = 21$

Step 1

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

$2 x - 6 = \pm \sqrt{21}$

Step 2

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

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

$2 x - 6 = \sqrt{21}$

Add $6$ to both sides of the equation.

$2 x = \sqrt{21} + 6$

Divide each term in $2 x = \sqrt{21} + 6$ by $2$ and simplify.

Divide each term in $2 x = \sqrt{21} + 6$ by $2$ .

$\frac{2 x}{2} = \frac{\sqrt{21}}{2} + \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\sqrt{21}}{2} + \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{21}}{2} + \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = \frac{\sqrt{21}}{2} + 3$

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

$2 x - 6 = - \sqrt{21}$

Add $6$ to both sides of the equation.

$2 x = - \sqrt{21} + 6$

Divide each term in $2 x = - \sqrt{21} + 6$ by $2$ and simplify.

Divide each term in $2 x = - \sqrt{21} + 6$ by $2$ .

$\frac{2 x}{2} = \frac{- \sqrt{21}}{2} + \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \sqrt{21}}{2} + \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{21}}{2} + \frac{6}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{21}}{2} + \frac{6}{2}$

Divide $6$ by $2$ .

$x = - \frac{\sqrt{21}}{2} + 3$

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

$x = \frac{\sqrt{21}}{2} + 3, - \frac{\sqrt{21}}{2} + 3$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{21}}{2} + 3, - \frac{\sqrt{21}}{2} + 3$

Decimal Form:

$x = 5.29128784 \dots, 0.70871215 \dots$

Solve Using the Square Root Property (2x-6)^2=21

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