Finite Math Examples

$4 x^{6} x (x) + 16 = 14$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Multiply $x^{6}$ by $x$ by adding the exponents.

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Step 1.1.1.1.1

Move $x$ .

$4 (x \cdot x^{6}) x + 16 = 14$

Step 1.1.1.1.2

Multiply $x$ by $x^{6}$ .

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Step 1.1.1.1.2.1

Raise $x$ to the power of $1$ .

$4 (x^{1} x^{6}) x + 16 = 14$

Step 1.1.1.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{1 + 6} x + 16 = 14$

Step 1.1.1.1.3

Add $1$ and $6$ .

$4 x^{7} x + 16 = 14$

Step 1.1.1.2

Multiply $x^{7}$ by $x$ by adding the exponents.

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Step 1.1.1.2.1

Move $x$ .

$4 (x \cdot x^{7}) + 16 = 14$

Step 1.1.1.2.2

Multiply $x$ by $x^{7}$ .

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Step 1.1.1.2.2.1

Raise $x$ to the power of $1$ .

$4 (x^{1} x^{7}) + 16 = 14$

Step 1.1.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{1 + 7} + 16 = 14$

Step 1.1.1.2.3

Add $1$ and $7$ .

$4 x^{8} + 16 = 14$

Step 1.2

Subtract $14$ from both sides of the equation.

$4 x^{8} + 16 - 14 = 0$

Step 1.3

Subtract $14$ from $16$ .

$4 x^{8} + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

$4 x^{8} = - 2$

Step 3

Divide each term in $4 x^{8} = - 2$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 x^{8} = - 2$ by $4$ .

$\frac{4 x^{8}}{4} = \frac{- 2}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 x^{8}}{4} = \frac{- 2}{4}$

Step 3.2.1.2

Divide $x^{8}$ by $1$ .

$x^{8} = \frac{- 2}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $- 2$ and $4$ .

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Step 3.3.1.1

Factor $2$ out of $- 2$ .

$x^{8} = \frac{2 (- 1)}{4}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $4$ .

$x^{8} = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 3.3.1.2.2

Cancel the common factor.

$x^{8} = \frac{2 \cdot - 1}{2 \cdot 2}$

Step 3.3.1.2.3

Rewrite the expression.

$x^{8} = \frac{- 1}{2}$

Step 3.3.2

Move the negative in front of the fraction.

$x^{8} = - \frac{1}{2}$

Step 4

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

$x = \pm \sqrt[8]{- \frac{1}{2}}$

Step 5

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

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Step 5.1

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

$x = \sqrt[8]{- \frac{1}{2}}$

Step 5.2

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

$x = - \sqrt[8]{- \frac{1}{2}}$

Step 5.3

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

$x = \sqrt[8]{- \frac{1}{2}}, - \sqrt[8]{- \frac{1}{2}}$