Solve 8x^2-80x-750

$$8 { x }^{ 2 } -80x-750$$

Factor

$$8\left(x-\left(-\frac{5\sqrt{19}}{2}+5\right)\right)\left(x-\left(\frac{5\sqrt{19}}{2}+5\right)\right)$$

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.

$$8x^{2}-80x-750=0$$

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.

$$x=\frac{-\left(-80\right)±\sqrt{\left(-80\right)^{2}-4\times 8\left(-750\right)}}{2\times 8}$$

Square -80.

$$x=\frac{-\left(-80\right)±\sqrt{6400-4\times 8\left(-750\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-\left(-80\right)±\sqrt{6400-32\left(-750\right)}}{2\times 8}$$

Multiply -32 times -750.

$$x=\frac{-\left(-80\right)±\sqrt{6400+24000}}{2\times 8}$$

Add 6400 to 24000.

$$x=\frac{-\left(-80\right)±\sqrt{30400}}{2\times 8}$$

Take the square root of 30400.

$$x=\frac{-\left(-80\right)±40\sqrt{19}}{2\times 8}$$

The opposite of -80 is 80.

$$x=\frac{80±40\sqrt{19}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{80±40\sqrt{19}}{16}$$

Now solve the equation x=\frac{80±40\sqrt{19}}{16} when ± is plus. Add 80 to 40\sqrt{19}.

$$x=\frac{40\sqrt{19}+80}{16}$$

Divide 80+40\sqrt{19} by 16.

$$x=\frac{5\sqrt{19}}{2}+5$$

Now solve the equation x=\frac{80±40\sqrt{19}}{16} when ± is minus. Subtract 40\sqrt{19} from 80.

$$x=\frac{80-40\sqrt{19}}{16}$$

Divide 80-40\sqrt{19} by 16.

$$x=-\frac{5\sqrt{19}}{2}+5$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 5+\frac{5\sqrt{19}}{2} for x_{1} and 5-\frac{5\sqrt{19}}{2} for x_{2}.

$$8x^{2}-80x-750=8\left(x-\left(\frac{5\sqrt{19}}{2}+5\right)\right)\left(x-\left(-\frac{5\sqrt{19}}{2}+5\right)\right)$$

Evaluate

$$8x^{2}-80x-750$$