Pre-Algebra Examples

$x^{2} + 14 x^{22} = 0$

Step 1

Factor $x^{2}$ out of $x^{2} + 14 x^{22}$ .

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Step 1.1

Multiply by $1$ .

$x^{2} \cdot 1 + 14 x^{22} = 0$

Step 1.2

Factor $x^{2}$ out of $14 x^{22}$ .

$x^{2} \cdot 1 + x^{2} (14 x^{20}) = 0$

Step 1.3

Factor $x^{2}$ out of $x^{2} \cdot 1 + x^{2} (14 x^{20})$ .

$x^{2} (1 + 14 x^{20}) = 0$

Step 2

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

$x^{2} = 0$

$1 + 14 x^{20} = 0$

Step 3

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

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Step 3.1

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

$x^{2} = 0$

Step 3.2

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

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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.

$x = \pm \sqrt{0}$

Step 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

$x = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 4

Set $1 + 14 x^{20}$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $1 + 14 x^{20}$ equal to $0$ .

$1 + 14 x^{20} = 0$

Step 4.2

Solve $1 + 14 x^{20} = 0$ for $x$ .

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$14 x^{20} = - 1$

Step 4.2.2

Divide each term in $14 x^{20} = - 1$ by $14$ and simplify.

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Step 4.2.2.1

Divide each term in $14 x^{20} = - 1$ by $14$ .

$\frac{14 x^{20}}{14} = \frac{- 1}{14}$

Step 4.2.2.2

Simplify the left side.

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Step 4.2.2.2.1

Cancel the common factor of $14$ .

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Step 4.2.2.2.1.1

Cancel the common factor.

$\frac{14 x^{20}}{14} = \frac{- 1}{14}$

Step 4.2.2.2.1.2

Divide $x^{20}$ by $1$ .

$x^{20} = \frac{- 1}{14}$

Step 4.2.2.3

Simplify the right side.

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Step 4.2.2.3.1

Move the negative in front of the fraction.

$x^{20} = - \frac{1}{14}$

Step 4.2.3

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

$x = \pm \sqrt[20]{- \frac{1}{14}}$

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.

$x = \sqrt[20]{- \frac{1}{14}}$

Step 4.2.4.2

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

$x = - \sqrt[20]{- \frac{1}{14}}$

Step 4.2.4.3

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

$x = \sqrt[20]{- \frac{1}{14}}, - \sqrt[20]{- \frac{1}{14}}$

Step 5

The final solution is all the values that make $x^{2} (1 + 14 x^{20}) = 0$ true.

$x = 0, \sqrt[20]{- \frac{1}{14}}, - \sqrt[20]{- \frac{1}{14}}$