Solve Using the Square Root Property -2(x-1)^2=36

$- 2 {(x - 1)}^{2} = 36$

Step 1

Divide each term in $- 2 {(x - 1)}^{2} = 36$ by $- 2$ and simplify.

Divide each term in $- 2 {(x - 1)}^{2} = 36$ by $- 2$ .

$\frac{- 2 {(x - 1)}^{2}}{- 2} = \frac{36}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 {(x - 1)}^{2}}{- 2} = \frac{36}{- 2}$

Divide ${(x - 1)}^{2}$ by $1$ .

${(x - 1)}^{2} = \frac{36}{- 2}$

Simplify the right side.

Divide $36$ by $- 2$ .

${(x - 1)}^{2} = - 18$

Step 2

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

$x - 1 = \pm \sqrt{- 18}$

Step 3

Simplify $\pm \sqrt{- 18}$ .

Rewrite $- 18$ as $- 1 (18)$ .

$x - 1 = \pm \sqrt{- 1 (18)}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$x - 1 = \pm \sqrt{- 1} \cdot \sqrt{18}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 1 = \pm i \cdot \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$x - 1 = \pm i \cdot \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$x - 1 = \pm i \cdot \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$x - 1 = \pm i \cdot (3 \sqrt{2})$

Move $3$ to the left of $i$ .

$x - 1 = \pm 3 i \sqrt{2}$

Step 4

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.

$x - 1 = 3 i \sqrt{2}$

Add $1$ to both sides of the equation.

$x = 3 i \sqrt{2} + 1$

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

$x - 1 = - 3 i \sqrt{2}$

Add $1$ to both sides of the equation.

$x = - 3 i \sqrt{2} + 1$

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

$x = 3 i \sqrt{2} + 1, - 3 i \sqrt{2} + 1$

Solve Using the Square Root Property -2(x-1)^2=36

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