Solve for x 3x^2+27=0

$3 x^{2} + 27 = 0$

Step 1

Subtract $27$ from both sides of the equation.

$3 x^{2} = - 27$

Step 2

Divide each term in $3 x^{2} = - 27$ by $3$ and simplify.

Divide each term in $3 x^{2} = - 27$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Divide $- 27$ by $3$ .

$x^{2} = - 9$

Step 3

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

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

Step 4

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

Rewrite $- 9$ as $- 1 (9)$ .

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

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{9}$

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

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

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

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

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

$x = \pm i \cdot 3$

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

$x = \pm 3 i$

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.

$x = 3 i$

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

$x = - 3 i$

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

$x = 3 i, - 3 i$