Solve 0.96mm=50m*2*80

$$0.96 mm = 50 m \times 2 \times 80$$

Solve for m

$$m = \frac{25000}{3} = 8333\frac{1}{3} \approx 8333.333333333$$

$$m=0$$

Steps Using Factoring

Multiply m and m to get m^{2}.

$$0.96m^{2}=50m\times 2\times 80$$

Multiply 50 and 2 to get 100.

$$0.96m^{2}=100m\times 80$$

Multiply 100 and 80 to get 8000.

$$0.96m^{2}=8000m$$

Subtract 8000m from both sides.

$$0.96m^{2}-8000m=0$$

Factor out m.

$$m\left(0.96m-8000\right)=0$$

To find equation solutions, solve m=0 and \frac{24m}{25}-8000=0.

$$m=0 m=\frac{25000}{3}$$

Steps Using the Quadratic Formula

Multiply m and m to get m^{2}.

$$0.96m^{2}=50m\times 2\times 80$$

Multiply 50 and 2 to get 100.

$$0.96m^{2}=100m\times 80$$

Multiply 100 and 80 to get 8000.

$$0.96m^{2}=8000m$$

Subtract 8000m from both sides.

$$0.96m^{2}-8000m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.96 for a, -8000 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-8000\right)±\sqrt{\left(-8000\right)^{2}}}{2\times 0.96}$$

Take the square root of \left(-8000\right)^{2}.

$$m=\frac{-\left(-8000\right)±8000}{2\times 0.96}$$

The opposite of -8000 is 8000.

$$m=\frac{8000±8000}{2\times 0.96}$$

Multiply 2 times 0.96.

$$m=\frac{8000±8000}{1.92}$$

Now solve the equation m=\frac{8000±8000}{1.92} when ± is plus. Add 8000 to 8000.

$$m=\frac{16000}{1.92}$$

Divide 16000 by 1.92 by multiplying 16000 by the reciprocal of 1.92.

$$m=\frac{25000}{3}$$

Now solve the equation m=\frac{8000±8000}{1.92} when ± is minus. Subtract 8000 from 8000.

$$m=\frac{0}{1.92}$$

Divide 0 by 1.92 by multiplying 0 by the reciprocal of 1.92.

$$m=0$$

The equation is now solved.

$$m=\frac{25000}{3} m=0$$

Steps for Completing the Square

Multiply m and m to get m^{2}.

$$0.96m^{2}=50m\times 2\times 80$$

Multiply 50 and 2 to get 100.

$$0.96m^{2}=100m\times 80$$

Multiply 100 and 80 to get 8000.

$$0.96m^{2}=8000m$$

Subtract 8000m from both sides.

$$0.96m^{2}-8000m=0$$

Divide both sides of the equation by 0.96, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.96m^{2}-8000m}{0.96}=\frac{0}{0.96}$$

Dividing by 0.96 undoes the multiplication by 0.96.

$$m^{2}+\left(-\frac{8000}{0.96}\right)m=\frac{0}{0.96}$$

Divide -8000 by 0.96 by multiplying -8000 by the reciprocal of 0.96.

$$m^{2}-\frac{25000}{3}m=\frac{0}{0.96}$$

Divide 0 by 0.96 by multiplying 0 by the reciprocal of 0.96.

$$m^{2}-\frac{25000}{3}m=0$$

Divide -\frac{25000}{3}, the coefficient of the x term, by 2 to get -\frac{12500}{3}. Then add the square of -\frac{12500}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{25000}{3}m+\left(-\frac{12500}{3}\right)^{2}=\left(-\frac{12500}{3}\right)^{2}$$

Square -\frac{12500}{3} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{25000}{3}m+\frac{156250000}{9}=\frac{156250000}{9}$$

Factor m^{2}-\frac{25000}{3}m+\frac{156250000}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{12500}{3}\right)^{2}=\frac{156250000}{9}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{12500}{3}\right)^{2}}=\sqrt{\frac{156250000}{9}}$$

Simplify.

$$m-\frac{12500}{3}=\frac{12500}{3} m-\frac{12500}{3}=-\frac{12500}{3}$$

Add \frac{12500}{3} to both sides of the equation.

$$m=\frac{25000}{3} m=0$$