Solve by Factoring 2x^4-48x^2=0

$2 x^{4} - 48 x^{2} = 0$

Step 1

Factor $2 x^{2}$ out of $2 x^{4} - 48 x^{2}$ .

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

$2 x^{2} (x^{2}) - 48 x^{2} = 0$

Factor $2 x^{2}$ out of $- 48 x^{2}$ .

$2 x^{2} (x^{2}) + 2 x^{2} (- 24) = 0$

Factor $2 x^{2}$ out of $2 x^{2} (x^{2}) + 2 x^{2} (- 24)$ .

$2 x^{2} (x^{2} - 24) = 0$

Step 2

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

$x^{2} = 0$

$x^{2} - 24 = 0$

Step 3

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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

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

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 4

Set $x^{2} - 24$ equal to $0$ and solve for $x$ .

Set $x^{2} - 24$ equal to $0$ .

$x^{2} - 24 = 0$

Solve $x^{2} - 24 = 0$ for $x$ .

Add $24$ to both sides of the equation.

$x^{2} = 24$

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

$x = \pm \sqrt{24}$

Simplify $\pm \sqrt{24}$ .

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \pm \sqrt{4 (6)}$

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

$x = \pm \sqrt{2^{2} \cdot 6}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{6}$

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.

$x = 2 \sqrt{6}$

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

$x = - 2 \sqrt{6}$

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

$x = 2 \sqrt{6}, - 2 \sqrt{6}$

Step 5

The final solution is all the values that make $2 x^{2} (x^{2} - 24) = 0$ true.

$x = 0, 2 \sqrt{6}, - 2 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 0, 2 \sqrt{6}, - 2 \sqrt{6}$

Decimal Form:

$x = 0, 4.89897948 \dots, - 4.89897948 \dots$

Solve by Factoring 2x^4-48x^2=0

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