Solve 9m^2+m

$$9 m ^ { 2 } + m$$

Factor

$$m\left(9m+1\right)$$

Solution Steps

Factor out m.

$$m\left(9m+1\right)$$

Steps Using the Quadratic Formula

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.

$$9m^{2}+m=0$$

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.

$$m=\frac{-1±\sqrt{1^{2}}}{2\times 9}$$

Take the square root of 1^{2}.

$$m=\frac{-1±1}{2\times 9}$$

Multiply 2 times 9.

$$m=\frac{-1±1}{18}$$

Now solve the equation m=\frac{-1±1}{18} when ± is plus. Add -1 to 1.

$$m=\frac{0}{18}$$

Divide 0 by 18.

$$m=0$$

Now solve the equation m=\frac{-1±1}{18} when ± is minus. Subtract 1 from -1.

$$m=-\frac{2}{18}$$

Reduce the fraction \frac{-2}{18} to lowest terms by extracting and canceling out 2.

$$m=-\frac{1}{9}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{1}{9} for x_{2}.

$$9m^{2}+m=9m\left(m-\left(-\frac{1}{9}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$9m^{2}+m=9m\left(m+\frac{1}{9}\right)$$

Add \frac{1}{9} to m by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$9m^{2}+m=9m\times \frac{9m+1}{9}$$

Cancel out 9, the greatest common factor in 9 and 9.

$$9m^{2}+m=m\left(9m+1\right)$$

Evaluate

$$m\left(9m+1\right)$$