Solve -x^2+325x-25000

$$- { x }^{ 2 } +325x-25000$$

Factor

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

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.

$$-x^{2}+325x-25000=0$$

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.

$$x=\frac{-325±\sqrt{325^{2}-4\left(-1\right)\left(-25000\right)}}{2\left(-1\right)}$$

Square 325.

$$x=\frac{-325±\sqrt{105625-4\left(-1\right)\left(-25000\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-325±\sqrt{105625+4\left(-25000\right)}}{2\left(-1\right)}$$

Multiply 4 times -25000.

$$x=\frac{-325±\sqrt{105625-100000}}{2\left(-1\right)}$$

Add 105625 to -100000.

$$x=\frac{-325±\sqrt{5625}}{2\left(-1\right)}$$

Take the square root of 5625.

$$x=\frac{-325±75}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-325±75}{-2}$$

Now solve the equation x=\frac{-325±75}{-2} when ± is plus. Add -325 to 75.

$$x=-\frac{250}{-2}$$

Divide -250 by -2.

$$x=125$$

Now solve the equation x=\frac{-325±75}{-2} when ± is minus. Subtract 75 from -325.

$$x=-\frac{400}{-2}$$

Divide -400 by -2.

$$x=200$$

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}.

$$-x^{2}+325x-25000=-\left(x-125\right)\left(x-200\right)$$

Evaluate

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