Solve by Factoring 6x^2+294=0

$6 x^{2} + 294 = 0$

Step 1

Factor $6$ out of $6 x^{2} + 294$ .

Factor $6$ out of $6 x^{2}$ .

$6 (x^{2}) + 294 = 0$

Factor $6$ out of $294$ .

$6 x^{2} + 6 \cdot 49 = 0$

Factor $6$ out of $6 x^{2} + 6 \cdot 49$ .

$6 (x^{2} + 49) = 0$

Step 2

Divide each term in $6 (x^{2} + 49) = 0$ by $6$ and simplify.

Divide each term in $6 (x^{2} + 49) = 0$ by $6$ .

$\frac{6 (x^{2} + 49)}{6} = \frac{0}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 (x^{2} + 49)}{6} = \frac{0}{6}$

Divide $x^{2} + 49$ by $1$ .

$x^{2} + 49 = \frac{0}{6}$

Simplify the right side.

Divide $0$ by $6$ .

$x^{2} + 49 = 0$

Step 3

Subtract $49$ from both sides of the equation.

$x^{2} = - 49$

Step 4

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

$x = \pm \sqrt{- 49}$

Step 5

Simplify $\pm \sqrt{- 49}$ .

Rewrite $- 49$ as $- 1 (49)$ .

$x = \pm \sqrt{- 1 (49)}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{49}$

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

$x = \pm i \cdot \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$x = \pm i \cdot \sqrt{7^{2}}$

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

$x = \pm i \cdot 7$

Move $7$ to the left of $i$ .

$x = \pm 7 i$

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.

$x = 7 i$

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

$x = - 7 i$

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

$x = 7 i, - 7 i$

Solve by Factoring 6x^2+294=0

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