Solve by Factoring 7x^4-28x^2=0

$7 x^{4} - 28 x^{2} = 0$

Factor $7 x^{2}$ out of $7 x^{4} - 28 x^{2}$ .

Tap for more steps…

Factor $7 x^{2}$ out of $7 x^{4}$ .

$7 x^{2} (x^{2}) - 28 x^{2} = 0$

Factor $7 x^{2}$ out of $- 28 x^{2}$ .

$7 x^{2} (x^{2}) + 7 x^{2} (- 4) = 0$

Factor $7 x^{2}$ out of $7 x^{2} (x^{2}) + 7 x^{2} (- 4)$ .

$7 x^{2} (x^{2} - 4) = 0$

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

$7 x^{2} (x^{2} - 2^{2}) = 0$

Factor.

Tap for more steps…

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$7 x^{2} ((x + 2) (x - 2)) = 0$

Remove unnecessary parentheses.

$7 x^{2} (x + 2) (x - 2) = 0$

Divide each term in $7 x^{2} (x + 2) (x - 2) = 0$ by $7$ .

$\frac{7 x^{2} (x + 2) (x - 2)}{7} = \frac{0}{7}$

Cancel the common factor of $7$ .

Tap for more steps…

Cancel the common factor.

$\frac{7 x^{2} (x + 2) (x - 2)}{7} = \frac{0}{7}$

Divide $(x^{2} (x + 2)) (x - 2)$ by $1$ .

$(x^{2} (x + 2)) (x - 2) = \frac{0}{7}$

Divide $0$ by $7$ .

$(x^{2} (x + 2)) (x - 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$x + 2 = 0$

$x - 2 = 0$

Set the first factor equal to $0$ and solve.

Tap for more steps…

Set the first factor equal to $0$ .

$x^{2} = 0$

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

$x = \pm \sqrt{0}$

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

Tap for more steps…

Simplify the right side of the equation.

Tap for more steps…

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

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

$x = \pm 0$

$\pm 0$ is equal to $0$ .

$x = 0$

Set the next factor equal to $0$ and solve.

Tap for more steps…

Set the next factor equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set the next factor equal to $0$ and solve.

Tap for more steps…

Set the next factor equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The final solution is all the values that make $\frac{7 x^{2} (x + 2) (x - 2)}{7} = \frac{0}{7}$ true.

$x = 0, - 2, 2$

Solve by Factoring 7x^4-28x^2=0

Need help with MATH HOMEWORK