Solve by Factoring 3x^2+300=0

$3 x^{2} + 300 = 0$

Step 1

Factor $3$ out of $3 x^{2} + 300$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) + 300 = 0$

Factor $3$ out of $300$ .

$3 x^{2} + 3 \cdot 100 = 0$

Factor $3$ out of $3 x^{2} + 3 \cdot 100$ .

$3 (x^{2} + 100) = 0$

Step 2

Divide each term in $3 (x^{2} + 100) = 0$ by $3$ and simplify.

Divide each term in $3 (x^{2} + 100) = 0$ by $3$ .

$\frac{3 (x^{2} + 100)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x^{2} + 100)}{3} = \frac{0}{3}$

Divide $x^{2} + 100$ by $1$ .

$x^{2} + 100 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x^{2} + 100 = 0$

Step 3

Subtract $100$ from both sides of the equation.

$x^{2} = - 100$

Step 4

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

$x = \pm \sqrt{- 100}$

Step 5

Simplify $\pm \sqrt{- 100}$ .

Rewrite $- 100$ as $- 1 (100)$ .

$x = \pm \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{100}$

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

$x = \pm i \cdot \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

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

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

$x = \pm i \cdot 10$

Move $10$ to the left of $i$ .

$x = \pm 10 i$

Step 6

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.

$x = 10 i$

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

$x = - 10 i$

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

$x = 10 i, - 10 i$

Solve by Factoring 3x^2+300=0

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