Solve -50x^2+370x

$$-50 { x }^{ 2 } +370x$$

Factor

$$10x\left(37-5x\right)$$

Solution Steps

Factor out 10.

$$10\left(-5x^{2}+37x\right)$$

Consider -5x^{2}+37x. Factor out x.

$$x\left(-5x+37\right)$$

Rewrite the complete factored expression.

$$10x\left(-5x+37\right)$$

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.

$$-50x^{2}+370x=0$$

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.

$$x=\frac{-370±\sqrt{370^{2}}}{2\left(-50\right)}$$

Take the square root of 370^{2}.

$$x=\frac{-370±370}{2\left(-50\right)}$$

Multiply 2 times -50.

$$x=\frac{-370±370}{-100}$$

Now solve the equation x=\frac{-370±370}{-100} when ± is plus. Add -370 to 370.

$$x=\frac{0}{-100}$$

Divide 0 by -100.

$$x=0$$

Now solve the equation x=\frac{-370±370}{-100} when ± is minus. Subtract 370 from -370.

$$x=-\frac{740}{-100}$$

Reduce the fraction \frac{-740}{-100} to lowest terms by extracting and canceling out 20.

$$x=\frac{37}{5}$$

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{37}{5} for x_{2}.

$$-50x^{2}+370x=-50x\left(x-\frac{37}{5}\right)$$

Subtract \frac{37}{5} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-50x^{2}+370x=-50x\times \frac{-5x+37}{-5}$$

Cancel out 5, the greatest common factor in -50 and -5.

$$-50x^{2}+370x=10x\left(-5x+37\right)$$

Evaluate

$$10x\left(37-5x\right)$$