Basic Math Examples

$2 a^{4} - 72 a^{2} = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

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

$2 {(a^{2})}^{2} - 72 a^{2} = 0$

Step 1.2

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

$2 u^{2} - 72 u = 0$

Step 1.3

Factor $2 u$ out of $2 u^{2} - 72 u$ .

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Step 1.3.1

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

$2 u (u) - 72 u = 0$

Step 1.3.2

Factor $2 u$ out of $- 72 u$ .

$2 u (u) + 2 u (- 36) = 0$

Step 1.3.3

Factor $2 u$ out of $2 u (u) + 2 u (- 36)$ .

$2 u (u - 36) = 0$

Step 1.4

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

$2 a^{2} (a^{2} - 36) = 0$

Step 2

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

$a^{2} = 0$

$a^{2} - 36 = 0$

Step 3

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

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Step 3.1

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

$a^{2} = 0$

Step 3.2

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

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Step 3.2.1

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

$a = \pm \sqrt{0}$

Step 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

$a = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$a = 0$

Step 4

Set $a^{2} - 36$ equal to $0$ and solve for $a$ .

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Step 4.1

Set $a^{2} - 36$ equal to $0$ .

$a^{2} - 36 = 0$

Step 4.2

Solve $a^{2} - 36 = 0$ for $a$ .

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Step 4.2.1

Add $36$ to both sides of the equation.

$a^{2} = 36$

Step 4.2.2

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

$a = \pm \sqrt{36}$

Step 4.2.3

Simplify $\pm \sqrt{36}$ .

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Step 4.2.3.1

Rewrite $36$ as $6^{2}$ .

$a = \pm \sqrt{6^{2}}$

Step 4.2.3.2

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

$a = \pm 6$

Step 4.2.4

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

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Step 4.2.4.1

First, use the positive value of the $\pm$ to find the first solution.

$a = 6$

Step 4.2.4.2

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

$a = - 6$

Step 4.2.4.3

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

$a = 6, - 6$

Step 5

The final solution is all the values that make $2 a^{2} (a^{2} - 36) = 0$ true.

$a = 0, 6, - 6$