Solve -10-8x-x^2

$$- 10 - 8 x - x ^ { 2 }$$

Factor

$$-\left(x-\left(-\sqrt{6}-4\right)\right)\left(x-\left(\sqrt{6}-4\right)\right)$$

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.

$$-x^{2}-8x-10=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\left(-10\right)}}{2\left(-1\right)}$$

Multiply 4 times -10.

$$x=\frac{-\left(-8\right)±\sqrt{64-40}}{2\left(-1\right)}$$

Add 64 to -40.

$$x=\frac{-\left(-8\right)±\sqrt{24}}{2\left(-1\right)}$$

Take the square root of 24.

$$x=\frac{-\left(-8\right)±2\sqrt{6}}{2\left(-1\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±2\sqrt{6}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{8±2\sqrt{6}}{-2}$$

Now solve the equation x=\frac{8±2\sqrt{6}}{-2} when ± is plus. Add 8 to 2\sqrt{6}.

$$x=\frac{2\sqrt{6}+8}{-2}$$

Divide 8+2\sqrt{6} by -2.

$$x=-\left(\sqrt{6}+4\right)$$

Now solve the equation x=\frac{8±2\sqrt{6}}{-2} when ± is minus. Subtract 2\sqrt{6} from 8.

$$x=\frac{8-2\sqrt{6}}{-2}$$

Divide 8-2\sqrt{6} by -2.

$$x=\sqrt{6}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\left(4+\sqrt{6}\right) for x_{1} and -4+\sqrt{6} for x_{2}.

$$-x^{2}-8x-10=-\left(x-\left(-\left(\sqrt{6}+4\right)\right)\right)\left(x-\left(\sqrt{6}-4\right)\right)$$

Evaluate

$$-x^{2}-8x-10$$