Solve -16a^2+2a

$$- 16 a ^ { 2 } + 2 a$$

Factor

$$2a\left(1-8a\right)$$

Solution Steps

Factor out 2.

$$2\left(-8a^{2}+a\right)$$

Consider -8a^{2}+a. Factor out a.

$$a\left(-8a+1\right)$$

Rewrite the complete factored expression.

$$2a\left(-8a+1\right)$$

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.

$$-16a^{2}+2a=0$$

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.

$$a=\frac{-2±\sqrt{2^{2}}}{2\left(-16\right)}$$

Take the square root of 2^{2}.

$$a=\frac{-2±2}{2\left(-16\right)}$$

Multiply 2 times -16.

$$a=\frac{-2±2}{-32}$$

Now solve the equation a=\frac{-2±2}{-32} when ± is plus. Add -2 to 2.

$$a=\frac{0}{-32}$$

Divide 0 by -32.

$$a=0$$

Now solve the equation a=\frac{-2±2}{-32} when ± is minus. Subtract 2 from -2.

$$a=-\frac{4}{-32}$$

Reduce the fraction \frac{-4}{-32} to lowest terms by extracting and canceling out 4.

$$a=\frac{1}{8}$$

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}{8} for x_{2}.

$$-16a^{2}+2a=-16a\left(a-\frac{1}{8}\right)$$

Subtract \frac{1}{8} from a by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-16a^{2}+2a=-16a\times \frac{-8a+1}{-8}$$

Cancel out 8, the greatest common factor in -16 and -8.

$$-16a^{2}+2a=2a\left(-8a+1\right)$$

Evaluate

$$2a\left(1-8a\right)$$