Solve 7a+14a^2=

$$7 a + 14 a ^ { 2 } =$$

Factor

$$7a\left(2a+1\right)$$

Solution Steps

Factor out 7.

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

Consider a+2a^{2}. Factor out a.

$$a\left(1+2a\right)$$

Rewrite the complete factored expression.

$$7a\left(2a+1\right)$$

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.

$$14a^{2}+7a=0$$

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.

$$a=\frac{-7±\sqrt{7^{2}}}{2\times 14}$$

Take the square root of 7^{2}.

$$a=\frac{-7±7}{2\times 14}$$

Multiply 2 times 14.

$$a=\frac{-7±7}{28}$$

Now solve the equation a=\frac{-7±7}{28} when ± is plus. Add -7 to 7.

$$a=\frac{0}{28}$$

Divide 0 by 28.

$$a=0$$

Now solve the equation a=\frac{-7±7}{28} when ± is minus. Subtract 7 from -7.

$$a=-\frac{14}{28}$$

Reduce the fraction \frac{-14}{28} to lowest terms by extracting and canceling out 14.

$$a=-\frac{1}{2}$$

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}{2} for x_{2}.

$$14a^{2}+7a=14a\left(a-\left(-\frac{1}{2}\right)\right)$$

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

$$14a^{2}+7a=14a\left(a+\frac{1}{2}\right)$$

Add \frac{1}{2} to a by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$14a^{2}+7a=14a\times \frac{2a+1}{2}$$

Cancel out 2, the greatest common factor in 14 and 2.

$$14a^{2}+7a=7a\left(2a+1\right)$$

Evaluate

$$7a\left(2a+1\right)$$