Solve Using the Square Root Property -2x^2+146=-34

$- 2 x^{2} + 146 = - 34$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $146$ from both sides of the equation.

$- 2 x^{2} = - 34 - 146$

Subtract $146$ from $- 34$ .

$- 2 x^{2} = - 180$

Step 2

Divide each term in $- 2 x^{2} = - 180$ by $- 2$ and simplify.

Divide each term in $- 2 x^{2} = - 180$ by $- 2$ .

$\frac{- 2 x^{2}}{- 2} = \frac{- 180}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x^{2}}{- 2} = \frac{- 180}{- 2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 180}{- 2}$

Simplify the right side.

Divide $- 180$ by $- 2$ .

$x^{2} = 90$

Step 3

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

$x = \pm \sqrt{90}$

Step 4

Simplify $\pm \sqrt{90}$ .

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$x = \pm \sqrt{9 (10)}$

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

$x = \pm \sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{10}$

Step 5

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.

$x = 3 \sqrt{10}$

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

$x = - 3 \sqrt{10}$

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

$x = 3 \sqrt{10}, - 3 \sqrt{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{10}, - 3 \sqrt{10}$

Decimal Form:

$x = 9.48683298 \dots, - 9.48683298 \dots$

Solve Using the Square Root Property -2x^2+146=-34

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