Solve -3-m/4=-2/5-m

$$- \frac { 3 - m } { 4 } = - \frac { 2 } { 5 - m }$$

Solve for m

$$m=1$$

$$m=7$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 4\left(m-5\right), the least common multiple of 4,5-m.

$$-\left(m-5\right)\left(3-m\right)=4\times 2$$

Use the distributive property to multiply m-5 by 3-m and combine like terms.

$$-\left(8m-m^{2}-15\right)=4\times 2$$

To find the opposite of 8m-m^{2}-15, find the opposite of each term.

$$-8m+m^{2}+15=4\times 2$$

Multiply 4 and 2 to get 8.

$$-8m+m^{2}+15=8$$

Subtract 8 from both sides.

$$-8m+m^{2}+15-8=0$$

Subtract 8 from 15 to get 7.

$$-8m+m^{2}+7=0$$

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.

$$m^{2}-8m+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 7}}{2}$$

Square -8.

$$m=\frac{-\left(-8\right)±\sqrt{64-4\times 7}}{2}$$

Multiply -4 times 7.

$$m=\frac{-\left(-8\right)±\sqrt{64-28}}{2}$$

Add 64 to -28.

$$m=\frac{-\left(-8\right)±\sqrt{36}}{2}$$

Take the square root of 36.

$$m=\frac{-\left(-8\right)±6}{2}$$

The opposite of -8 is 8.

$$m=\frac{8±6}{2}$$

Now solve the equation m=\frac{8±6}{2} when ± is plus. Add 8 to 6.

$$m=\frac{14}{2}$$

Divide 14 by 2.

$$m=7$$

Now solve the equation m=\frac{8±6}{2} when ± is minus. Subtract 6 from 8.

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

Divide 2 by 2.

$$m=1$$

The equation is now solved.

$$m=7 m=1$$

Steps for Completing the Square

Variable m cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 4\left(m-5\right), the least common multiple of 4,5-m.

$$-\left(m-5\right)\left(3-m\right)=4\times 2$$

Use the distributive property to multiply m-5 by 3-m and combine like terms.

$$-\left(8m-m^{2}-15\right)=4\times 2$$

To find the opposite of 8m-m^{2}-15, find the opposite of each term.

$$-8m+m^{2}+15=4\times 2$$

Multiply 4 and 2 to get 8.

$$-8m+m^{2}+15=8$$

Subtract 15 from both sides.

$$-8m+m^{2}=8-15$$

Subtract 15 from 8 to get -7.

$$-8m+m^{2}=-7$$

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.

$$m^{2}-8m=-7$$

Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-8m+\left(-4\right)^{2}=-7+\left(-4\right)^{2}$$

Square -4.

$$m^{2}-8m+16=-7+16$$

Add -7 to 16.

$$m^{2}-8m+16=9$$

Factor m^{2}-8m+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}.

$$\left(m-4\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-4\right)^{2}}=\sqrt{9}$$

Simplify.

$$m-4=3 m-4=-3$$

Add 4 to both sides of the equation.

$$m=7 m=1$$