Solve -x^2-8x+15

$$- { x }^{ 2 } -8x+15$$

Factor

$$-\left(x-\left(-\sqrt{31}-4\right)\right)\left(x-\left(\sqrt{31}-4\right)\right)$$

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.

$$-x^{2}-8x+15=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 15}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\times 15}}{2\left(-1\right)}$$

Multiply 4 times 15.

$$x=\frac{-\left(-8\right)±\sqrt{64+60}}{2\left(-1\right)}$$

Add 64 to 60.

$$x=\frac{-\left(-8\right)±\sqrt{124}}{2\left(-1\right)}$$

Take the square root of 124.

$$x=\frac{-\left(-8\right)±2\sqrt{31}}{2\left(-1\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±2\sqrt{31}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{8±2\sqrt{31}}{-2}$$

Now solve the equation x=\frac{8±2\sqrt{31}}{-2} when ± is plus. Add 8 to 2\sqrt{31}.

$$x=\frac{2\sqrt{31}+8}{-2}$$

Divide 8+2\sqrt{31} by -2.

$$x=-\left(\sqrt{31}+4\right)$$

Now solve the equation x=\frac{8±2\sqrt{31}}{-2} when ± is minus. Subtract 2\sqrt{31} from 8.

$$x=\frac{8-2\sqrt{31}}{-2}$$

Divide 8-2\sqrt{31} by -2.

$$x=\sqrt{31}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\left(4+\sqrt{31}\right) for x_{1} and -4+\sqrt{31} for x_{2}.

$$-x^{2}-8x+15=-\left(x-\left(-\left(\sqrt{31}+4\right)\right)\right)\left(x-\left(\sqrt{31}-4\right)\right)$$

Evaluate

$$15-8x-x^{2}$$