Solve 10x^2+30x-8000

$$10 { x }^{ 2 } +30x-8000$$

Factor

$$10\left(x-\frac{-\sqrt{3209}-3}{2}\right)\left(x-\frac{\sqrt{3209}-3}{2}\right)$$

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.

$$10x^{2}+30x-8000=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\times 10\left(-8000\right)}}{2\times 10}$$

Square 30.

$$x=\frac{-30±\sqrt{900-4\times 10\left(-8000\right)}}{2\times 10}$$

Multiply -4 times 10.

$$x=\frac{-30±\sqrt{900-40\left(-8000\right)}}{2\times 10}$$

Multiply -40 times -8000.

$$x=\frac{-30±\sqrt{900+320000}}{2\times 10}$$

Add 900 to 320000.

$$x=\frac{-30±\sqrt{320900}}{2\times 10}$$

Take the square root of 320900.

$$x=\frac{-30±10\sqrt{3209}}{2\times 10}$$

Multiply 2 times 10.

$$x=\frac{-30±10\sqrt{3209}}{20}$$

Now solve the equation x=\frac{-30±10\sqrt{3209}}{20} when ± is plus. Add -30 to 10\sqrt{3209}.

$$x=\frac{10\sqrt{3209}-30}{20}$$

Divide -30+10\sqrt{3209} by 20.

$$x=\frac{\sqrt{3209}-3}{2}$$

Now solve the equation x=\frac{-30±10\sqrt{3209}}{20} when ± is minus. Subtract 10\sqrt{3209} from -30.

$$x=\frac{-10\sqrt{3209}-30}{20}$$

Divide -30-10\sqrt{3209} by 20.

$$x=\frac{-\sqrt{3209}-3}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{3209}}{2} for x_{1} and \frac{-3-\sqrt{3209}}{2} for x_{2}.

$$10x^{2}+30x-8000=10\left(x-\frac{\sqrt{3209}-3}{2}\right)\left(x-\frac{-\sqrt{3209}-3}{2}\right)$$

Evaluate

$$10\left(x^{2}+3x-800\right)$$