Solve 15-4x^2-8x

$$15 - 4 x ^ { 2 } - 8 x$$

Factor

$$-4\left(x-\left(-\frac{\sqrt{19}}{2}-1\right)\right)\left(x-\left(\frac{\sqrt{19}}{2}-1\right)\right)$$

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.

$$-4x^{2}-8x+15=0$$

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.

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

Square -8.

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

Multiply -4 times -4.

$$x=\frac{-\left(-8\right)±\sqrt{64+16\times 15}}{2\left(-4\right)}$$

Multiply 16 times 15.

$$x=\frac{-\left(-8\right)±\sqrt{64+240}}{2\left(-4\right)}$$

Add 64 to 240.

$$x=\frac{-\left(-8\right)±\sqrt{304}}{2\left(-4\right)}$$

Take the square root of 304.

$$x=\frac{-\left(-8\right)±4\sqrt{19}}{2\left(-4\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±4\sqrt{19}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{8±4\sqrt{19}}{-8}$$

Now solve the equation x=\frac{8±4\sqrt{19}}{-8} when ± is plus. Add 8 to 4\sqrt{19}.

$$x=\frac{4\sqrt{19}+8}{-8}$$

Divide 8+4\sqrt{19} by -8.

$$x=-\frac{\sqrt{19}}{2}-1$$

Now solve the equation x=\frac{8±4\sqrt{19}}{-8} when ± is minus. Subtract 4\sqrt{19} from 8.

$$x=\frac{8-4\sqrt{19}}{-8}$$

Divide 8-4\sqrt{19} by -8.

$$x=\frac{\sqrt{19}}{2}-1$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -1-\frac{\sqrt{19}}{2} for x_{1} and -1+\frac{\sqrt{19}}{2} for x_{2}.

$$-4x^{2}-8x+15=-4\left(x-\left(-\frac{\sqrt{19}}{2}-1\right)\right)\left(x-\left(\frac{\sqrt{19}}{2}-1\right)\right)$$

Evaluate

$$15-8x-4x^{2}$$