Solve Using the Square Root Property 9x^2-3=-152

$9 x^{2} - 3 = - 152$

Step 1

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

Add $3$ to both sides of the equation.

$9 x^{2} = - 152 + 3$

Add $- 152$ and $3$ .

$9 x^{2} = - 149$

Step 2

Divide each term in $9 x^{2} = - 149$ by $9$ and simplify.

Divide each term in $9 x^{2} = - 149$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{- 149}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{- 149}{9}$

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

$x^{2} = \frac{- 149}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{149}{9}$

Step 3

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

$x = \pm \sqrt{- \frac{149}{9}}$

Step 4

Simplify $\pm \sqrt{- \frac{149}{9}}$ .

Rewrite $- \frac{149}{9}$ as ${(\frac{i}{3})}^{2} \cdot 149$ .

Rewrite $- 1$ as $i^{2}$ .

$x = \pm \sqrt{i^{2} \frac{149}{9}}$

Factor the perfect power $1^{2}$ out of $149$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 149}{9}}$

Factor the perfect power $3^{2}$ out of $9$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 149}{3^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} \cdot 149}{3^{2} \cdot 1}$ .

$x = \pm \sqrt{i^{2} ({(\frac{1}{3})}^{2} \cdot 149)}$

Rewrite $i^{2} {(\frac{1}{3})}^{2}$ as ${(\frac{i}{3})}^{2}$ .

$x = \pm \sqrt{{(\frac{i}{3})}^{2} \cdot 149}$

Pull terms out from under the radical.

$x = \pm \frac{i}{3} \sqrt{149}$

Combine $\frac{i}{3}$ and $\sqrt{149}$ .

$x = \pm \frac{i \sqrt{149}}{3}$

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.

$x = \frac{i \sqrt{149}}{3}$

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

$x = - \frac{i \sqrt{149}}{3}$

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

$x = \frac{i \sqrt{149}}{3}, - \frac{i \sqrt{149}}{3}$

Solve Using the Square Root Property 9x^2-3=-152

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