Solve 20m^2-40m=0

$$20 m ^ { 2 } - 40 m = 0$$

Solve for m

$$m=2$$

$$m=0$$

Steps Using Factoring

Factor out m.

$$m\left(20m-40\right)=0$$

To find equation solutions, solve m=0 and 20m-40=0.

$$m=0 m=2$$

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.

$$20m^{2}-40m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, -40 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}}}{2\times 20}$$

Take the square root of \left(-40\right)^{2}.

$$m=\frac{-\left(-40\right)±40}{2\times 20}$$

The opposite of -40 is 40.

$$m=\frac{40±40}{2\times 20}$$

Multiply 2 times 20.

$$m=\frac{40±40}{40}$$

Now solve the equation m=\frac{40±40}{40} when ± is plus. Add 40 to 40.

$$m=\frac{80}{40}$$

Divide 80 by 40.

$$m=2$$

Now solve the equation m=\frac{40±40}{40} when ± is minus. Subtract 40 from 40.

$$m=\frac{0}{40}$$

Divide 0 by 40.

$$m=0$$

The equation is now solved.

$$m=2 m=0$$

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.

$$20m^{2}-40m=0$$

Divide both sides by 20.

$$\frac{20m^{2}-40m}{20}=\frac{0}{20}$$

Dividing by 20 undoes the multiplication by 20.

$$m^{2}+\left(-\frac{40}{20}\right)m=\frac{0}{20}$$

Divide -40 by 20.

$$m^{2}-2m=\frac{0}{20}$$

Divide 0 by 20.

$$m^{2}-2m=0$$

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

$$m^{2}-2m+1=1$$

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

$$\left(m-1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$m-1=1 m-1=-1$$

Add 1 to both sides of the equation.

$$m=2 m=0$$