Solve (4-2m)(-2m-1)=50

$$( 4 - 2 m ) ( - 2 m - 1 ) = 50$$

Solve for m

$$m = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$m=-3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4-2m by -2m-1 and combine like terms.

$$-6m-4+4m^{2}=50$$

Subtract 50 from both sides.

$$-6m-4+4m^{2}-50=0$$

Subtract 50 from -4 to get -54.

$$-6m-54+4m^{2}=0$$

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.

$$4m^{2}-6m-54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, -6 for b, and -54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 4\left(-54\right)}}{2\times 4}$$

Square -6.

$$m=\frac{-\left(-6\right)±\sqrt{36-4\times 4\left(-54\right)}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{-\left(-6\right)±\sqrt{36-16\left(-54\right)}}{2\times 4}$$

Multiply -16 times -54.

$$m=\frac{-\left(-6\right)±\sqrt{36+864}}{2\times 4}$$

Add 36 to 864.

$$m=\frac{-\left(-6\right)±\sqrt{900}}{2\times 4}$$

Take the square root of 900.

$$m=\frac{-\left(-6\right)±30}{2\times 4}$$

The opposite of -6 is 6.

$$m=\frac{6±30}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{6±30}{8}$$

Now solve the equation m=\frac{6±30}{8} when ± is plus. Add 6 to 30.

$$m=\frac{36}{8}$$

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$m=\frac{9}{2}$$

Now solve the equation m=\frac{6±30}{8} when ± is minus. Subtract 30 from 6.

$$m=-\frac{24}{8}$$

Divide -24 by 8.

$$m=-3$$

The equation is now solved.

$$m=\frac{9}{2} m=-3$$

Steps for Completing the Square

Use the distributive property to multiply 4-2m by -2m-1 and combine like terms.

$$-6m-4+4m^{2}=50$$

Add 4 to both sides.

$$-6m+4m^{2}=50+4$$

Add 50 and 4 to get 54.

$$-6m+4m^{2}=54$$

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.

$$4m^{2}-6m=54$$

Divide both sides by 4.

$$\frac{4m^{2}-6m}{4}=\frac{54}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$m^{2}+\left(-\frac{6}{4}\right)m=\frac{54}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

$$m^{2}-\frac{3}{2}m=\frac{54}{4}$$

Reduce the fraction \frac{54}{4} to lowest terms by extracting and canceling out 2.

$$m^{2}-\frac{3}{2}m=\frac{27}{2}$$

Divide -\frac{3}{2}, the coefficient of the x term, by 2 to get -\frac{3}{4}. Then add the square of -\frac{3}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{3}{2}m+\left(-\frac{3}{4}\right)^{2}=\frac{27}{2}+\left(-\frac{3}{4}\right)^{2}$$

Square -\frac{3}{4} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{3}{2}m+\frac{9}{16}=\frac{27}{2}+\frac{9}{16}$$

Add \frac{27}{2} to \frac{9}{16} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$m^{2}-\frac{3}{2}m+\frac{9}{16}=\frac{225}{16}$$

Factor m^{2}-\frac{3}{2}m+\frac{9}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{3}{4}\right)^{2}=\frac{225}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{3}{4}\right)^{2}}=\sqrt{\frac{225}{16}}$$

Simplify.

$$m-\frac{3}{4}=\frac{15}{4} m-\frac{3}{4}=-\frac{15}{4}$$

Add \frac{3}{4} to both sides of the equation.

$$m=\frac{9}{2} m=-3$$