Solve for x 36x^3-x=0

$36 x^{3} - x = 0$

Step 1

Factor the left side of the equation.

Factor $x$ out of $36 x^{3} - x$ .

Factor $x$ out of $36 x^{3}$ .

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

Factor $x$ out of $- x$ .

$x (36 x^{2}) + x \cdot - 1 = 0$

Factor $x$ out of $x (36 x^{2}) + x \cdot - 1$ .

$x (36 x^{2} - 1) = 0$

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

$x ({(6 x)}^{2} - 1) = 0$

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

$x ({(6 x)}^{2} - 1^{2}) = 0$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 6 x$ and $b = 1$ .

$x ((6 x + 1) (6 x - 1)) = 0$

Remove unnecessary parentheses.

$x (6 x + 1) (6 x - 1) = 0$

Step 2

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

$x = 0$

$6 x + 1 = 0$

$6 x - 1 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $6 x + 1$ equal to $0$ and solve for $x$ .

Set $6 x + 1$ equal to $0$ .

$6 x + 1 = 0$

Solve $6 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$6 x = - 1$

Divide each term in $6 x = - 1$ by $6$ and simplify.

Divide each term in $6 x = - 1$ by $6$ .

$\frac{6 x}{6} = \frac{- 1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 1}{6}$

Divide $x$ by $1$ .

$x = \frac{- 1}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{6}$

Step 5

Set $6 x - 1$ equal to $0$ and solve for $x$ .

Set $6 x - 1$ equal to $0$ .

$6 x - 1 = 0$

Solve $6 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$6 x = 1$

Divide each term in $6 x = 1$ by $6$ and simplify.

Divide each term in $6 x = 1$ by $6$ .

$\frac{6 x}{6} = \frac{1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{1}{6}$

Divide $x$ by $1$ .

$x = \frac{1}{6}$

Step 6

The final solution is all the values that make $x (6 x + 1) (6 x - 1) = 0$ true.

$x = 0, - \frac{1}{6}, \frac{1}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{1}{6}, \frac{1}{6}$

Decimal Form:

$x = 0, - 0.1\overline{6}, 0.1\overline{6}$

Solve for x 36x^3-x=0

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