Algebra Examples

$5 x^{4} - 20 x^{2} = 0$

Step 1

Factor $5 x^{2}$ out of $5 x^{4} - 20 x^{2}$ .

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Step 1.1

Factor $5 x^{2}$ out of $5 x^{4}$ .

$5 x^{2} (x^{2}) - 20 x^{2} = 0$

Step 1.2

Factor $5 x^{2}$ out of $- 20 x^{2}$ .

$5 x^{2} (x^{2}) + 5 x^{2} (- 4) = 0$

Step 1.3

Factor $5 x^{2}$ out of $5 x^{2} (x^{2}) + 5 x^{2} (- 4)$ .

$5 x^{2} (x^{2} - 4) = 0$

Step 2

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

$5 x^{2} (x^{2} - 2^{2}) = 0$

Step 3

Factor.

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Step 3.1

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 $b = 2$ .

$5 x^{2} ((x + 2) (x - 2)) = 0$

Step 3.2

Remove unnecessary parentheses.

$5 x^{2} (x + 2) (x - 2) = 0$

Step 4

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

$x^{2} = 0$

$x + 2 = 0$

$x - 2 = 0$

Step 5

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

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Step 5.1

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

$x^{2} = 0$

Step 5.2

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

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Step 5.2.1

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

$x = \pm \sqrt{0}$

Step 5.2.2

Simplify $\pm \sqrt{0}$ .

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Step 5.2.2.1

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

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

Step 5.2.2.2

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

$x = \pm 0$

Step 5.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 6

Set $x + 2$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 6.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 7.2

Add $2$ to both sides of the equation.

$x = 2$

Step 8

The final solution is all the values that make $5 x^{2} (x + 2) (x - 2) = 0$ true.

$x = 0, - 2, 2$