Solve by Factoring 3x^2+48=0

$3 x^{2} + 48 = 0$

Step 1

Factor $3$ out of $3 x^{2} + 48$ .

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

$3 (x^{2}) + 48 = 0$

Factor $3$ out of $48$ .

$3 x^{2} + 3 \cdot 16 = 0$

Factor $3$ out of $3 x^{2} + 3 \cdot 16$ .

$3 (x^{2} + 16) = 0$

Step 2

Divide each term in $3 (x^{2} + 16) = 0$ by $3$ and simplify.

Divide each term in $3 (x^{2} + 16) = 0$ by $3$ .

$\frac{3 (x^{2} + 16)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x^{2} + 16)}{3} = \frac{0}{3}$

Divide $x^{2} + 16$ by $1$ .

$x^{2} + 16 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x^{2} + 16 = 0$

Step 3

Subtract $16$ from both sides of the equation.

$x^{2} = - 16$

Step 4

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

$x = \pm \sqrt{- 16}$

Step 5

Simplify $\pm \sqrt{- 16}$ .

Rewrite $- 16$ as $- 1 (16)$ .

$x = \pm \sqrt{- 1 (16)}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{16}$

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

$x = \pm i \cdot \sqrt{16}$

Rewrite $16$ as $4^{2}$ .

$x = \pm i \cdot \sqrt{4^{2}}$

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

$x = \pm i \cdot 4$

Move $4$ to the left of $i$ .

$x = \pm 4 i$

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.

$x = 4 i$

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

$x = - 4 i$

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

$x = 4 i, - 4 i$

Solve by Factoring 3x^2+48=0

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