Solve for x 4x^4=12x^2

$4 x^{4} = 12 x^{2}$

Step 1

Subtract $12 x^{2}$ from both sides of the equation.

$4 x^{4} - 12 x^{2} = 0$

Step 2

Factor the left side of the equation.

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$4 {(x^{2})}^{2} - 12 x^{2} = 0$

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$4 u^{2} - 12 u = 0$

Factor $4 u$ out of $4 u^{2} - 12 u$ .

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

$4 u (u) - 12 u = 0$

Factor $4 u$ out of $- 12 u$ .

$4 u (u) + 4 u (- 3) = 0$

Factor $4 u$ out of $4 u (u) + 4 u (- 3)$ .

$4 u (u - 3) = 0$

Replace all occurrences of $u$ with $x^{2}$ .

$4 x^{2} (x^{2} - 3) = 0$

Step 3

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

$x^{2} = 0$

$x^{2} - 3 = 0$

Step 4

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 5

Set $x^{2} - 3$ equal to $0$ and solve for $x$ .

Set $x^{2} - 3$ equal to $0$ .

$x^{2} - 3 = 0$

Solve $x^{2} - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$x^{2} = 3$

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

$x = \pm \sqrt{3}$

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.

$x = \sqrt{3}$

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

$x = - \sqrt{3}$

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

$x = \sqrt{3}, - \sqrt{3}$

Step 6

The final solution is all the values that make $4 x^{2} (x^{2} - 3) = 0$ true.

$x = 0, \sqrt{3}, - \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 0, 1.73205080 \dots, - 1.73205080 \dots$

Solve for x 4x^4=12x^2

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