Solve for x 2/5x^2-1/4x=0

$\frac{2}{5} x^{2} - \frac{1}{4} x = 0$

Step 1

Simplify each term.

Combine $\frac{2}{5}$ and $x^{2}$ .

$\frac{2 x^{2}}{5} - \frac{1}{4} x = 0$

Combine $x$ and $\frac{1}{4}$ .

$\frac{2 x^{2}}{5} - \frac{x}{4} = 0$

Step 2

Multiply each term in $\frac{2 x^{2}}{5} - \frac{x}{4} = 0$ by $20$ to eliminate the fractions.

Multiply each term in $\frac{2 x^{2}}{5} - \frac{x}{4} = 0$ by $20$ .

$\frac{2 x^{2}}{5} \cdot 20 - \frac{x}{4} \cdot 20 = 0 \cdot 20$

Simplify the left side.

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{2 x^{2}}{5} \cdot (5 (4)) - \frac{x}{4} \cdot 20 = 0 \cdot 20$

Cancel the common factor.

$\frac{2 x^{2}}{5} \cdot (5 \cdot 4) - \frac{x}{4} \cdot 20 = 0 \cdot 20$

Rewrite the expression.

$2 x^{2} \cdot 4 - \frac{x}{4} \cdot 20 = 0 \cdot 20$

Multiply $4$ by $2$ .

$8 x^{2} - \frac{x}{4} \cdot 20 = 0 \cdot 20$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$8 x^{2} + \frac{- x}{4} \cdot 20 = 0 \cdot 20$

Factor $4$ out of $20$ .

$8 x^{2} + \frac{- x}{4} \cdot (4 (5)) = 0 \cdot 20$

Cancel the common factor.

$8 x^{2} + \frac{- x}{4} \cdot (4 \cdot 5) = 0 \cdot 20$

Rewrite the expression.

$8 x^{2} - x \cdot 5 = 0 \cdot 20$

Multiply $5$ by $- 1$ .

$8 x^{2} - 5 x = 0 \cdot 20$

Simplify the right side.

Multiply $0$ by $20$ .

$8 x^{2} - 5 x = 0$

Step 3

Factor $x$ out of $8 x^{2} - 5 x$ .

Factor $x$ out of $8 x^{2}$ .

$x (8 x) - 5 x = 0$

Factor $x$ out of $- 5 x$ .

$x (8 x) + x \cdot - 5 = 0$

Factor $x$ out of $x (8 x) + x \cdot - 5$ .

$x (8 x - 5) = 0$

Step 4

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

$x = 0$

$8 x - 5 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $8 x - 5$ equal to $0$ and solve for $x$ .

Set $8 x - 5$ equal to $0$ .

$8 x - 5 = 0$

Solve $8 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$8 x = 5$

Divide each term in $8 x = 5$ by $8$ and simplify.

Divide each term in $8 x = 5$ by $8$ .

$\frac{8 x}{8} = \frac{5}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{5}{8}$

Divide $x$ by $1$ .

$x = \frac{5}{8}$

Step 7

The final solution is all the values that make $x (8 x - 5) = 0$ true.

$x = 0, \frac{5}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{5}{8}$

Decimal Form:

$x = 0, 0.625$

Solve for x 2/5x^2-1/4x=0

Related Questions

Support LCMGCF.com by disabling your adblocker.