Solve Using the Square Root Property (2x-2)^2=30

${(2 x - 2)}^{2} = 30$

Step 1

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

$2 x - 2 = \pm \sqrt{30}$

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.

$2 x - 2 = \sqrt{30}$

Add $2$ to both sides of the equation.

$2 x = \sqrt{30} + 2$

Divide each term in $2 x = \sqrt{30} + 2$ by $2$ and simplify.

Divide each term in $2 x = \sqrt{30} + 2$ by $2$ .

$\frac{2 x}{2} = \frac{\sqrt{30}}{2} + \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\sqrt{30}}{2} + \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{30}}{2} + \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = \frac{\sqrt{30}}{2} + 1$

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

$2 x - 2 = - \sqrt{30}$

Add $2$ to both sides of the equation.

$2 x = - \sqrt{30} + 2$

Divide each term in $2 x = - \sqrt{30} + 2$ by $2$ and simplify.

Divide each term in $2 x = - \sqrt{30} + 2$ by $2$ .

$\frac{2 x}{2} = \frac{- \sqrt{30}}{2} + \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \sqrt{30}}{2} + \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{30}}{2} + \frac{2}{2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{30}}{2} + \frac{2}{2}$

Divide $2$ by $2$ .

$x = - \frac{\sqrt{30}}{2} + 1$

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

$x = \frac{\sqrt{30}}{2} + 1, - \frac{\sqrt{30}}{2} + 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{30}}{2} + 1, - \frac{\sqrt{30}}{2} + 1$

Decimal Form:

$x = 3.73861278 \dots, - 1.73861278 \dots$

Solve Using the Square Root Property (2x-2)^2=30

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