Solve 30x^2+100x-280000

$$30 { x }^{ 2 } +100x-280000$$

Factor

$$30\left(x-\frac{-5\sqrt{3361}-5}{3}\right)\left(x-\frac{5\sqrt{3361}-5}{3}\right)$$

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.

$$30x^{2}+100x-280000=0$$

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.

$$x=\frac{-100±\sqrt{100^{2}-4\times 30\left(-280000\right)}}{2\times 30}$$

Square 100.

$$x=\frac{-100±\sqrt{10000-4\times 30\left(-280000\right)}}{2\times 30}$$

Multiply -4 times 30.

$$x=\frac{-100±\sqrt{10000-120\left(-280000\right)}}{2\times 30}$$

Multiply -120 times -280000.

$$x=\frac{-100±\sqrt{10000+33600000}}{2\times 30}$$

Add 10000 to 33600000.

$$x=\frac{-100±\sqrt{33610000}}{2\times 30}$$

Take the square root of 33610000.

$$x=\frac{-100±100\sqrt{3361}}{2\times 30}$$

Multiply 2 times 30.

$$x=\frac{-100±100\sqrt{3361}}{60}$$

Now solve the equation x=\frac{-100±100\sqrt{3361}}{60} when ± is plus. Add -100 to 100\sqrt{3361}.

$$x=\frac{100\sqrt{3361}-100}{60}$$

Divide -100+100\sqrt{3361} by 60.

$$x=\frac{5\sqrt{3361}-5}{3}$$

Now solve the equation x=\frac{-100±100\sqrt{3361}}{60} when ± is minus. Subtract 100\sqrt{3361} from -100.

$$x=\frac{-100\sqrt{3361}-100}{60}$$

Divide -100-100\sqrt{3361} by 60.

$$x=\frac{-5\sqrt{3361}-5}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+5\sqrt{3361}}{3} for x_{1} and \frac{-5-5\sqrt{3361}}{3} for x_{2}.

$$30x^{2}+100x-280000=30\left(x-\frac{5\sqrt{3361}-5}{3}\right)\left(x-\frac{-5\sqrt{3361}-5}{3}\right)$$

Evaluate

$$30x^{2}+100x-280000$$