Algebra Examples

$x = \frac{1}{3} (6 + \log (2.1)) x^{3}$

Step 1

Simplify $\frac{1}{3} \cdot ((6 + \log (2.1)) x^{3})$ .

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Step 1.1

Log base $10$ of $2.1$ is approximately $0.32221929$ .

$x = \frac{1}{3} \cdot ((6 + 0.32221929) x^{3})$

Step 1.2

Add $6$ and $0.32221929$ .

$x = \frac{1}{3} \cdot (6.32221929 x^{3})$

Step 1.3

Multiply $\frac{1}{3} (6.32221929 x^{3})$ .

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Step 1.3.1

Combine $6.32221929$ and $\frac{1}{3}$ .

$x = \frac{6.32221929}{3} x^{3}$

Step 1.3.2

Combine $\frac{6.32221929}{3}$ and $x^{3}$ .

$x = \frac{6.32221929 x^{3}}{3}$

Step 1.4

Factor $6.32221929$ out of $6.32221929 x^{3}$ .

$x = \frac{6.32221929 (x^{3})}{3}$

Step 1.5

Factor $3$ out of $3$ .

$x = \frac{6.32221929 (x^{3})}{3 (1)}$

Step 1.6

Separate fractions.

$x = \frac{6.32221929}{3} \cdot \frac{x^{3}}{1}$

Step 1.7

Divide $6.32221929$ by $3$ .

$x = 2.10740643 \frac{x^{3}}{1}$

Step 1.8

Divide $x^{3}$ by $1$ .

$x = 2.10740643 x^{3}$

Step 2

Subtract $2.10740643 x^{3}$ from both sides of the equation.

$x - 2.10740643 x^{3} = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $x$ out of $x - 2.10740643 x^{3}$ .

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Step 3.1.1

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

$x - 2.10740643 x^{3} = 0$

Step 3.1.2

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - 2.10740643 x^{3} = 0$

Step 3.1.3

Factor $x$ out of $- 2.10740643 x^{3}$ .

$x \cdot 1 + x (- 2.10740643 x^{2}) = 0$

Step 3.1.4

Factor $x$ out of $x \cdot 1 + x (- 2.10740643 x^{2})$ .

$x (1 - 2.10740643 x^{2}) = 0$

Step 3.2

Rewrite $1$ as $1^{2}$ .

$x (1^{2} - 2.10740643 x^{2}) = 0$

Step 3.3

Rewrite $2.10740643 x^{2}$ as ${(1.45169088 x)}^{2}$ .

$x (1^{2} - {(1.45169088 x)}^{2}) = 0$

Step 3.4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 1.45169088 x$ .

$x ((1 + 1.45169088 x) (1 - (1.45169088 x))) = 0$

Step 3.5

Factor.

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Step 3.5.1

Multiply $1.45169088$ by $- 1$ .

$x ((1 + 1.45169088 x) (1 - 1.45169088 x)) = 0$

Step 3.5.2

Remove unnecessary parentheses.

$x (1 + 1.45169088 x) (1 - 1.45169088 x) = 0$

Step 4

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

$x = 0$

$1 + 1.45169088 x = 0$

$1 - 1.45169088 x = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $1 + 1.45169088 x$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $1 + 1.45169088 x$ equal to $0$ .

$1 + 1.45169088 x = 0$

Step 6.2

Solve $1 + 1.45169088 x = 0$ for $x$ .

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Step 6.2.1

Subtract $1$ from both sides of the equation.

$1.45169088 x = - 1$

Step 6.2.2

Divide each term in $1.45169088 x = - 1$ by $1.45169088$ and simplify.

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Step 6.2.2.1

Divide each term in $1.45169088 x = - 1$ by $1.45169088$ .

$\frac{1.45169088 x}{1.45169088} = \frac{- 1}{1.45169088}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $1.45169088$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{1.45169088 x}{1.45169088} = \frac{- 1}{1.45169088}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{1.45169088}$

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Divide $- 1$ by $1.45169088$ .

$x = - 0.68885188$

Step 7

Set $1 - 1.45169088 x$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $1 - 1.45169088 x$ equal to $0$ .

$1 - 1.45169088 x = 0$

Step 7.2

Solve $1 - 1.45169088 x = 0$ for $x$ .

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Step 7.2.1

Subtract $1$ from both sides of the equation.

$- 1.45169088 x = - 1$

Step 7.2.2

Divide each term in $- 1.45169088 x = - 1$ by $- 1.45169088$ and simplify.

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Step 7.2.2.1

Divide each term in $- 1.45169088 x = - 1$ by $- 1.45169088$ .

$\frac{- 1.45169088 x}{- 1.45169088} = \frac{- 1}{- 1.45169088}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $- 1.45169088$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{- 1.45169088 x}{- 1.45169088} = \frac{- 1}{- 1.45169088}$

Step 7.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 1.45169088}$

Step 7.2.2.3

Simplify the right side.

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Step 7.2.2.3.1

Divide $- 1$ by $- 1.45169088$ .

$x = 0.68885188$

Step 8

The final solution is all the values that make $x (1 + 1.45169088 x) (1 - 1.45169088 x) = 0$ true.

$x = 0, - 0.68885188, 0.68885188$