Solve -x^2+25x+15

$$- { x }^{ 2 } +25x+15$$

Factor

$$-\left(x-\frac{25-\sqrt{685}}{2}\right)\left(x-\frac{\sqrt{685}+25}{2}\right)$$

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.

$$-x^{2}+25x+15=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Square 25.

$$x=\frac{-25±\sqrt{625-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-25±\sqrt{625+4\times 15}}{2\left(-1\right)}$$

Multiply 4 times 15.

$$x=\frac{-25±\sqrt{625+60}}{2\left(-1\right)}$$

Add 625 to 60.

$$x=\frac{-25±\sqrt{685}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-25±\sqrt{685}}{-2}$$

Now solve the equation x=\frac{-25±\sqrt{685}}{-2} when ± is plus. Add -25 to \sqrt{685}.

$$x=\frac{\sqrt{685}-25}{-2}$$

Divide -25+\sqrt{685} by -2.

$$x=\frac{25-\sqrt{685}}{2}$$

Now solve the equation x=\frac{-25±\sqrt{685}}{-2} when ± is minus. Subtract \sqrt{685} from -25.

$$x=\frac{-\sqrt{685}-25}{-2}$$

Divide -25-\sqrt{685} by -2.

$$x=\frac{\sqrt{685}+25}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{25-\sqrt{685}}{2} for x_{1} and \frac{25+\sqrt{685}}{2} for x_{2}.

$$-x^{2}+25x+15=-\left(x-\frac{25-\sqrt{685}}{2}\right)\left(x-\frac{\sqrt{685}+25}{2}\right)$$

Evaluate

$$15+25x-x^{2}$$