Solve for x 18x^3=50x

$18 x^{3} = 50 x$

Step 1

Subtract $50 x$ from both sides of the equation.

$18 x^{3} - 50 x = 0$

Step 2

Factor the left side of the equation.

Factor $2 x$ out of $18 x^{3} - 50 x$ .

Factor $2 x$ out of $18 x^{3}$ .

$2 x (9 x^{2}) - 50 x = 0$

Factor $2 x$ out of $- 50 x$ .

$2 x (9 x^{2}) + 2 x (- 25) = 0$

Factor $2 x$ out of $2 x (9 x^{2}) + 2 x (- 25)$ .

$2 x (9 x^{2} - 25) = 0$

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$2 x ({(3 x)}^{2} - 25) = 0$

Rewrite $25$ as $5^{2}$ .

$2 x ({(3 x)}^{2} - 5^{2}) = 0$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = 5$ .

$2 x ((3 x + 5) (3 x - 5)) = 0$

Remove unnecessary parentheses.

$2 x (3 x + 5) (3 x - 5) = 0$

Step 3

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

$x = 0$

$3 x + 5 = 0$

$3 x - 5 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $3 x + 5$ equal to $0$ and solve for $x$ .

Set $3 x + 5$ equal to $0$ .

$3 x + 5 = 0$

Solve $3 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$3 x = - 5$

Divide each term in $3 x = - 5$ by $3$ and simplify.

Divide each term in $3 x = - 5$ by $3$ .

$\frac{3 x}{3} = \frac{- 5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 5}{3}$

Divide $x$ by $1$ .

$x = \frac{- 5}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{3}$

Step 6

Set $3 x - 5$ equal to $0$ and solve for $x$ .

Set $3 x - 5$ equal to $0$ .

$3 x - 5 = 0$

Solve $3 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$3 x = 5$

Divide each term in $3 x = 5$ by $3$ and simplify.

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 7

The final solution is all the values that make $2 x (3 x + 5) (3 x - 5) = 0$ true.

$x = 0, - \frac{5}{3}, \frac{5}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{5}{3}, \frac{5}{3}$

Decimal Form:

$x = 0, - 1.\overline{6}, 1.\overline{6}$

Mixed Number Form:

$x = 0, - 1 \frac{2}{3}, 1 \frac{2}{3}$

Solve for x 18x^3=50x

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