Solve 50x-2x^2

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

Factor

$$2x\left(25-x\right)$$

Solution Steps

Factor out 2.

$$2\left(25x-x^{2}\right)$$

Consider 25x-x^{2}. Factor out x.

$$x\left(25-x\right)$$

Rewrite the complete factored expression.

$$2x\left(-x+25\right)$$

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.

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

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.

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

Take the square root of 50^{2}.

$$x=\frac{-50±50}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-50±50}{-4}$$

Now solve the equation x=\frac{-50±50}{-4} when ± is plus. Add -50 to 50.

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

Now solve the equation x=\frac{-50±50}{-4} when ± is minus. Subtract 50 from -50.

$$x=-\frac{100}{-4}$$

Divide -100 by -4.

$$x=25$$

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 25 for x_{2}.

$$-2x^{2}+50x=-2x\left(x-25\right)$$

Evaluate

$$2x\left(25-x\right)$$