Solve Using the Square Root Property 1/3x^2-10=-37

$\frac{1}{3} x^{2} - 10 = - 37$

Step 1

Combine $\frac{1}{3}$ and $x^{2}$ .

$\frac{x^{2}}{3} - 10 = - 37$

Step 2

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

Add $10$ to both sides of the equation.

$\frac{x^{2}}{3} = - 37 + 10$

Add $- 37$ and $10$ .

$\frac{x^{2}}{3} = - 27$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{x^{2}}{3} = 3 \cdot - 27$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x^{2}}{3} = 3 \cdot - 27$

Rewrite the expression.

$x^{2} = 3 \cdot - 27$

Simplify the right side.

Multiply $3$ by $- 27$ .

$x^{2} = - 81$

Step 5

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

$x = \pm \sqrt{- 81}$

Step 6

Simplify $\pm \sqrt{- 81}$ .

Rewrite $- 81$ as $- 1 (81)$ .

$x = \pm \sqrt{- 1 (81)}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{81}$

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

$x = \pm i \cdot \sqrt{81}$

Rewrite $81$ as $9^{2}$ .

$x = \pm i \cdot \sqrt{9^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i \cdot 9$

Move $9$ to the left of $i$ .

$x = \pm 9 i$

Step 7

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.

$x = 9 i$

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

$x = - 9 i$

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

$x = 9 i, - 9 i$

Solve Using the Square Root Property 1/3x^2-10=-37

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