Solve 96x^2-x=0

$$96 x ^ { 2 } - x = 0$$

Solve for x

$$x=\frac{1}{96}\approx 0.010416667$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(96x-1\right)=0$$

To find equation solutions, solve x=0 and 96x-1=0.

$$x=0 x=\frac{1}{96}$$

Steps Using the Quadratic Formula

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.

$$96x^{2}-x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 96 for a, -1 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 96}$$

Take the square root of 1.

$$x=\frac{-\left(-1\right)±1}{2\times 96}$$

The opposite of -1 is 1.

$$x=\frac{1±1}{2\times 96}$$

Multiply 2 times 96.

$$x=\frac{1±1}{192}$$

Now solve the equation x=\frac{1±1}{192} when ± is plus. Add 1 to 1.

$$x=\frac{2}{192}$$

Reduce the fraction \frac{2}{192} to lowest terms by extracting and canceling out 2.

$$x=\frac{1}{96}$$

Now solve the equation x=\frac{1±1}{192} when ± is minus. Subtract 1 from 1.

$$x=\frac{0}{192}$$

Divide 0 by 192.

$$x=0$$

The equation is now solved.

$$x=\frac{1}{96} x=0$$

Steps for Completing the Square

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.

$$96x^{2}-x=0$$

Divide both sides by 96.

$$\frac{96x^{2}-x}{96}=\frac{0}{96}$$

Dividing by 96 undoes the multiplication by 96.

$$x^{2}-\frac{1}{96}x=\frac{0}{96}$$

Divide 0 by 96.

$$x^{2}-\frac{1}{96}x=0$$

Divide -\frac{1}{96}, the coefficient of the x term, by 2 to get -\frac{1}{192}. Then add the square of -\frac{1}{192} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1}{96}x+\left(-\frac{1}{192}\right)^{2}=\left(-\frac{1}{192}\right)^{2}$$

Square -\frac{1}{192} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1}{96}x+\frac{1}{36864}=\frac{1}{36864}$$

Factor x^{2}-\frac{1}{96}x+\frac{1}{36864}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{192}\right)^{2}=\frac{1}{36864}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{192}\right)^{2}}=\sqrt{\frac{1}{36864}}$$

Simplify.

$$x-\frac{1}{192}=\frac{1}{192} x-\frac{1}{192}=-\frac{1}{192}$$

Add \frac{1}{192} to both sides of the equation.

$$x=\frac{1}{96} x=0$$