Solve -28x^2+35x

$$- 28 x ^ { 2 } + 35 x$$

Factor

$$7x\left(5-4x\right)$$

Solution Steps

Factor out 7.

$$7\left(-4x^{2}+5x\right)$$

Consider -4x^{2}+5x. Factor out x.

$$x\left(-4x+5\right)$$

Rewrite the complete factored expression.

$$7x\left(-4x+5\right)$$

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.

$$-28x^{2}+35x=0$$

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.

$$x=\frac{-35±\sqrt{35^{2}}}{2\left(-28\right)}$$

Take the square root of 35^{2}.

$$x=\frac{-35±35}{2\left(-28\right)}$$

Multiply 2 times -28.

$$x=\frac{-35±35}{-56}$$

Now solve the equation x=\frac{-35±35}{-56} when ± is plus. Add -35 to 35.

$$x=\frac{0}{-56}$$

Divide 0 by -56.

$$x=0$$

Now solve the equation x=\frac{-35±35}{-56} when ± is minus. Subtract 35 from -35.

$$x=-\frac{70}{-56}$$

Reduce the fraction \frac{-70}{-56} to lowest terms by extracting and canceling out 14.

$$x=\frac{5}{4}$$

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{5}{4} for x_{2}.

$$-28x^{2}+35x=-28x\left(x-\frac{5}{4}\right)$$

Subtract \frac{5}{4} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-28x^{2}+35x=-28x\times \frac{-4x+5}{-4}$$

Cancel out 4, the greatest common factor in -28 and -4.

$$-28x^{2}+35x=7x\left(-4x+5\right)$$

Evaluate

$$7x\left(5-4x\right)$$