Solve Using the Square Root Property (3x-6)^2=33

${(3 x - 6)}^{2} = 33$

Step 1

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

$3 x - 6 = \pm \sqrt{33}$

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.

$3 x - 6 = \sqrt{33}$

Add $6$ to both sides of the equation.

$3 x = \sqrt{33} + 6$

Divide each term in $3 x = \sqrt{33} + 6$ by $3$ and simplify.

Divide each term in $3 x = \sqrt{33} + 6$ by $3$ .

$\frac{3 x}{3} = \frac{\sqrt{33}}{3} + \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\sqrt{33}}{3} + \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{33}}{3} + \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x = \frac{\sqrt{33}}{3} + 2$

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

$3 x - 6 = - \sqrt{33}$

Add $6$ to both sides of the equation.

$3 x = - \sqrt{33} + 6$

Divide each term in $3 x = - \sqrt{33} + 6$ by $3$ and simplify.

Divide each term in $3 x = - \sqrt{33} + 6$ by $3$ .

$\frac{3 x}{3} = \frac{- \sqrt{33}}{3} + \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \sqrt{33}}{3} + \frac{6}{3}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{33}}{3} + \frac{6}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{33}}{3} + \frac{6}{3}$

Divide $6$ by $3$ .

$x = - \frac{\sqrt{33}}{3} + 2$

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

$x = \frac{\sqrt{33}}{3} + 2, - \frac{\sqrt{33}}{3} + 2$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{33}}{3} + 2, - \frac{\sqrt{33}}{3} + 2$

Decimal Form:

$x = 3.91485421 \dots, 0.08514578 \dots$

Solve Using the Square Root Property (3x-6)^2=33

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