Solve 35m^2+5m

$$35 m ^ { 2 } + 5 m$$

Factor

$$5m\left(7m+1\right)$$

Solution Steps

Factor out 5.

$$5\left(7m^{2}+m\right)$$

Consider 7m^{2}+m. Factor out m.

$$m\left(7m+1\right)$$

Rewrite the complete factored expression.

$$5m\left(7m+1\right)$$

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.

$$35m^{2}+5m=0$$

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.

$$m=\frac{-5±\sqrt{5^{2}}}{2\times 35}$$

Take the square root of 5^{2}.

$$m=\frac{-5±5}{2\times 35}$$

Multiply 2 times 35.

$$m=\frac{-5±5}{70}$$

Now solve the equation m=\frac{-5±5}{70} when ± is plus. Add -5 to 5.

$$m=\frac{0}{70}$$

Divide 0 by 70.

$$m=0$$

Now solve the equation m=\frac{-5±5}{70} when ± is minus. Subtract 5 from -5.

$$m=-\frac{10}{70}$$

Reduce the fraction \frac{-10}{70} to lowest terms by extracting and canceling out 10.

$$m=-\frac{1}{7}$$

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}{7} for x_{2}.

$$35m^{2}+5m=35m\left(m-\left(-\frac{1}{7}\right)\right)$$

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

$$35m^{2}+5m=35m\left(m+\frac{1}{7}\right)$$

Add \frac{1}{7} to m by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$35m^{2}+5m=35m\times \frac{7m+1}{7}$$

Cancel out 7, the greatest common factor in 35 and 7.

$$35m^{2}+5m=5m\left(7m+1\right)$$

Evaluate

$$5m\left(7m+1\right)$$