Solve 2m-14quaddiv1/m^2-3m-28

$$2 m - 14 \quad \div \frac { 1 } { m ^ { 2 } - 3 m - 28 }$$

Evaluate

$$392+44m-14m^{2}$$

Solution Steps

Divide 14 by \frac{1}{m^{2}-3m-28} by multiplying 14 by the reciprocal of \frac{1}{m^{2}-3m-28}.

$$2m-14\left(m^{2}-3m-28\right)$$

Use the distributive property to multiply 14 by m^{2}-3m-28.

$$2m-\left(14m^{2}-42m-392\right)$$

To find the opposite of 14m^{2}-42m-392, find the opposite of each term.

$$2m-14m^{2}+42m+392$$

Combine 2m and 42m to get 44m.

$$44m-14m^{2}+392$$

Factor

$$-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$

Steps Using the Quadratic Formula

Divide 14 by \frac{1}{m^{2}-3m-28} by multiplying 14 by the reciprocal of \frac{1}{m^{2}-3m-28}.

$$factor(2m-14\left(m^{2}-3m-28\right))$$

Use the distributive property to multiply 14 by m^{2}-3m-28.

$$factor(2m-\left(14m^{2}-42m-392\right))$$

To find the opposite of 14m^{2}-42m-392, find the opposite of each term.

$$factor(2m-14m^{2}+42m+392)$$

Combine 2m and 42m to get 44m.

$$factor(44m-14m^{2}+392)$$

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-14m^{2}+44m+392=0$$

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.

$$m=\frac{-44±\sqrt{44^{2}-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

Square 44.

$$m=\frac{-44±\sqrt{1936-4\left(-14\right)\times 392}}{2\left(-14\right)}$$

Multiply -4 times -14.

$$m=\frac{-44±\sqrt{1936+56\times 392}}{2\left(-14\right)}$$

Multiply 56 times 392.

$$m=\frac{-44±\sqrt{1936+21952}}{2\left(-14\right)}$$

Add 1936 to 21952.

$$m=\frac{-44±\sqrt{23888}}{2\left(-14\right)}$$

Take the square root of 23888.

$$m=\frac{-44±4\sqrt{1493}}{2\left(-14\right)}$$

Multiply 2 times -14.

$$m=\frac{-44±4\sqrt{1493}}{-28}$$

Now solve the equation m=\frac{-44±4\sqrt{1493}}{-28} when ± is plus. Add -44 to 4\sqrt{1493}.

$$m=\frac{4\sqrt{1493}-44}{-28}$$

Divide -44+4\sqrt{1493} by -28.

$$m=\frac{11-\sqrt{1493}}{7}$$

Now solve the equation m=\frac{-44±4\sqrt{1493}}{-28} when ± is minus. Subtract 4\sqrt{1493} from -44.

$$m=\frac{-4\sqrt{1493}-44}{-28}$$

Divide -44-4\sqrt{1493} by -28.

$$m=\frac{\sqrt{1493}+11}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{11-\sqrt{1493}}{7} for x_{1} and \frac{11+\sqrt{1493}}{7} for x_{2}.

$$-14m^{2}+44m+392=-14\left(m-\frac{11-\sqrt{1493}}{7}\right)\left(m-\frac{\sqrt{1493}+11}{7}\right)$$