Solve x^2*48/x=2/15

$${ x }^{ 2 } \times \frac{ 48 }{ x } = \frac{ 2 }{ 15 }$$

Solve for x

$$x=\frac{1}{360}\approx 0.002777778$$

Steps Using Factoring

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15x, the least common multiple of x,15.

$$x^{2}\times 15\times 48=2x$$

Multiply 15 and 48 to get 720.

$$x^{2}\times 720=2x$$

Subtract 2x from both sides.

$$x^{2}\times 720-2x=0$$

Factor out x.

$$x\left(720x-2\right)=0$$

To find equation solutions, solve x=0 and 720x-2=0.

$$x=0 x=\frac{1}{360}$$

Variable x cannot be equal to 0.

$$x=\frac{1}{360}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15x, the least common multiple of x,15.

$$x^{2}\times 15\times 48=2x$$

Multiply 15 and 48 to get 720.

$$x^{2}\times 720=2x$$

Subtract 2x from both sides.

$$x^{2}\times 720-2x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$720x^{2}-2x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 720 for a, -2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\times 720}$$

Take the square root of \left(-2\right)^{2}.

$$x=\frac{-\left(-2\right)±2}{2\times 720}$$

The opposite of -2 is 2.

$$x=\frac{2±2}{2\times 720}$$

Multiply 2 times 720.

$$x=\frac{2±2}{1440}$$

Now solve the equation x=\frac{2±2}{1440} when ± is plus. Add 2 to 2.

$$x=\frac{4}{1440}$$

Reduce the fraction \frac{4}{1440} to lowest terms by extracting and canceling out 4.

$$x=\frac{1}{360}$$

Now solve the equation x=\frac{2±2}{1440} when ± is minus. Subtract 2 from 2.

$$x=\frac{0}{1440}$$

Divide 0 by 1440.

$$x=0$$

The equation is now solved.

$$x=\frac{1}{360} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1}{360}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15x, the least common multiple of x,15.

$$x^{2}\times 15\times 48=2x$$

Multiply 15 and 48 to get 720.

$$x^{2}\times 720=2x$$

Subtract 2x from both sides.

$$x^{2}\times 720-2x=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$720x^{2}-2x=0$$

Divide both sides by 720.

$$\frac{720x^{2}-2x}{720}=\frac{0}{720}$$

Dividing by 720 undoes the multiplication by 720.

$$x^{2}+\left(-\frac{2}{720}\right)x=\frac{0}{720}$$

Reduce the fraction \frac{-2}{720} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{1}{360}x=\frac{0}{720}$$

Divide 0 by 720.

$$x^{2}-\frac{1}{360}x=0$$

Divide -\frac{1}{360}, the coefficient of the x term, by 2 to get -\frac{1}{720}. Then add the square of -\frac{1}{720} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{360}x+\left(-\frac{1}{720}\right)^{2}=\left(-\frac{1}{720}\right)^{2}$$

Square -\frac{1}{720} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{360}x+\frac{1}{518400}=\frac{1}{518400}$$

Factor x^{2}-\frac{1}{360}x+\frac{1}{518400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{720}\right)^{2}=\frac{1}{518400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{720}\right)^{2}}=\sqrt{\frac{1}{518400}}$$

Simplify.

$$x-\frac{1}{720}=\frac{1}{720} x-\frac{1}{720}=-\frac{1}{720}$$

Add \frac{1}{720} to both sides of the equation.

$$x=\frac{1}{360} x=0$$

Variable x cannot be equal to 0.

$$x=\frac{1}{360}$$