Solve (9m+2)+(4m^2+6m)

$$( 9 m + 2 ) + ( 4 m ^ { 2 } + 6 m )$$

Factor

$$4\left(m-\frac{-\sqrt{193}-15}{8}\right)\left(m-\frac{\sqrt{193}-15}{8}\right)$$

Steps Using the Quadratic Formula

Combine 9m and 6m to get 15m.

$$factor(15m+2+4m^{2})$$

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.

$$4m^{2}+15m+2=0$$

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.

$$m=\frac{-15±\sqrt{15^{2}-4\times 4\times 2}}{2\times 4}$$

Square 15.

$$m=\frac{-15±\sqrt{225-4\times 4\times 2}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{-15±\sqrt{225-16\times 2}}{2\times 4}$$

Multiply -16 times 2.

$$m=\frac{-15±\sqrt{225-32}}{2\times 4}$$

Add 225 to -32.

$$m=\frac{-15±\sqrt{193}}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{-15±\sqrt{193}}{8}$$

Now solve the equation m=\frac{-15±\sqrt{193}}{8} when ± is plus. Add -15 to \sqrt{193}.

$$m=\frac{\sqrt{193}-15}{8}$$

Now solve the equation m=\frac{-15±\sqrt{193}}{8} when ± is minus. Subtract \sqrt{193} from -15.

$$m=\frac{-\sqrt{193}-15}{8}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-15+\sqrt{193}}{8} for x_{1} and \frac{-15-\sqrt{193}}{8} for x_{2}.

$$4m^{2}+15m+2=4\left(m-\frac{\sqrt{193}-15}{8}\right)\left(m-\frac{-\sqrt{193}-15}{8}\right)$$

Evaluate

$$4m^{2}+15m+2$$

Solution Steps

Combine 9m and 6m to get 15m.

$$15m+2+4m^{2}$$