Solve -36x^2+8x

$$- 36 x ^ { 2 } + 8 x$$

Factor

$$4x\left(2-9x\right)$$

Solution Steps

Factor out 4.

$$4\left(-9x^{2}+2x\right)$$

Consider -9x^{2}+2x. Factor out x.

$$x\left(-9x+2\right)$$

Rewrite the complete factored expression.

$$4x\left(-9x+2\right)$$

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.

$$-36x^{2}+8x=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}}}{2\left(-36\right)}$$

Take the square root of 8^{2}.

$$x=\frac{-8±8}{2\left(-36\right)}$$

Multiply 2 times -36.

$$x=\frac{-8±8}{-72}$$

Now solve the equation x=\frac{-8±8}{-72} when ± is plus. Add -8 to 8.

$$x=\frac{0}{-72}$$

Divide 0 by -72.

$$x=0$$

Now solve the equation x=\frac{-8±8}{-72} when ± is minus. Subtract 8 from -8.

$$x=-\frac{16}{-72}$$

Reduce the fraction \frac{-16}{-72} to lowest terms by extracting and canceling out 8.

$$x=\frac{2}{9}$$

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{2}{9} for x_{2}.

$$-36x^{2}+8x=-36x\left(x-\frac{2}{9}\right)$$

Subtract \frac{2}{9} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-36x^{2}+8x=-36x\times \frac{-9x+2}{-9}$$

Cancel out 9, the greatest common factor in -36 and -9.

$$-36x^{2}+8x=4x\left(-9x+2\right)$$

Evaluate

$$4x\left(2-9x\right)$$