Solve -80x^2+26000x-2000000

$$-80 { x }^{ 2 } +26000x-2000000$$

Factor

$$-80\left(x-200\right)\left(x-125\right)$$

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.

$$-80x^{2}+26000x-2000000=0$$

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.

$$x=\frac{-26000±\sqrt{26000^{2}-4\left(-80\right)\left(-2000000\right)}}{2\left(-80\right)}$$

Square 26000.

$$x=\frac{-26000±\sqrt{676000000-4\left(-80\right)\left(-2000000\right)}}{2\left(-80\right)}$$

Multiply -4 times -80.

$$x=\frac{-26000±\sqrt{676000000+320\left(-2000000\right)}}{2\left(-80\right)}$$

Multiply 320 times -2000000.

$$x=\frac{-26000±\sqrt{676000000-640000000}}{2\left(-80\right)}$$

Add 676000000 to -640000000.

$$x=\frac{-26000±\sqrt{36000000}}{2\left(-80\right)}$$

Take the square root of 36000000.

$$x=\frac{-26000±6000}{2\left(-80\right)}$$

Multiply 2 times -80.

$$x=\frac{-26000±6000}{-160}$$

Now solve the equation x=\frac{-26000±6000}{-160} when ± is plus. Add -26000 to 6000.

$$x=-\frac{20000}{-160}$$

Divide -20000 by -160.

$$x=125$$

Now solve the equation x=\frac{-26000±6000}{-160} when ± is minus. Subtract 6000 from -26000.

$$x=-\frac{32000}{-160}$$

Divide -32000 by -160.

$$x=200$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 125 for x_{1} and 200 for x_{2}.

$$-80x^{2}+26000x-2000000=-80\left(x-125\right)\left(x-200\right)$$

Evaluate

$$-80\left(x-200\right)\left(x-125\right)$$