Solve -64x+128x^2=

$$-64x+128 { x }^{ 2 } =$$

Factor

$$64x\left(2x-1\right)$$

Solution Steps

Factor out 64.

$$64\left(-x+2x^{2}\right)$$

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

$$x\left(-1+2x\right)$$

Rewrite the complete factored expression.

$$64x\left(2x-1\right)$$

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.

$$128x^{2}-64x=0$$

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.

$$x=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}}}{2\times 128}$$

Take the square root of \left(-64\right)^{2}.

$$x=\frac{-\left(-64\right)±64}{2\times 128}$$

The opposite of -64 is 64.

$$x=\frac{64±64}{2\times 128}$$

Multiply 2 times 128.

$$x=\frac{64±64}{256}$$

Now solve the equation x=\frac{64±64}{256} when ± is plus. Add 64 to 64.

$$x=\frac{128}{256}$$

Reduce the fraction \frac{128}{256} to lowest terms by extracting and canceling out 128.

$$x=\frac{1}{2}$$

Now solve the equation x=\frac{64±64}{256} when ± is minus. Subtract 64 from 64.

$$x=\frac{0}{256}$$

Divide 0 by 256.

$$x=0$$

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

$$128x^{2}-64x=128\left(x-\frac{1}{2}\right)x$$

Subtract \frac{1}{2} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$128x^{2}-64x=128\times \frac{2x-1}{2}x$$

Cancel out 2, the greatest common factor in 128 and 2.

$$128x^{2}-64x=64\left(2x-1\right)x$$

Evaluate

$$64x\left(2x-1\right)$$