Solve 108x^2+200x-20400

$$108 { x }^{ 2 } +200x-20400$$

Factor

$$108\left(x-\frac{-5\sqrt{5533}-25}{27}\right)\left(x-\frac{5\sqrt{5533}-25}{27}\right)$$

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.

$$108x^{2}+200x-20400=0$$

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.

$$x=\frac{-200±\sqrt{200^{2}-4\times 108\left(-20400\right)}}{2\times 108}$$

Square 200.

$$x=\frac{-200±\sqrt{40000-4\times 108\left(-20400\right)}}{2\times 108}$$

Multiply -4 times 108.

$$x=\frac{-200±\sqrt{40000-432\left(-20400\right)}}{2\times 108}$$

Multiply -432 times -20400.

$$x=\frac{-200±\sqrt{40000+8812800}}{2\times 108}$$

Add 40000 to 8812800.

$$x=\frac{-200±\sqrt{8852800}}{2\times 108}$$

Take the square root of 8852800.

$$x=\frac{-200±40\sqrt{5533}}{2\times 108}$$

Multiply 2 times 108.

$$x=\frac{-200±40\sqrt{5533}}{216}$$

Now solve the equation x=\frac{-200±40\sqrt{5533}}{216} when ± is plus. Add -200 to 40\sqrt{5533}.

$$x=\frac{40\sqrt{5533}-200}{216}$$

Divide -200+40\sqrt{5533} by 216.

$$x=\frac{5\sqrt{5533}-25}{27}$$

Now solve the equation x=\frac{-200±40\sqrt{5533}}{216} when ± is minus. Subtract 40\sqrt{5533} from -200.

$$x=\frac{-40\sqrt{5533}-200}{216}$$

Divide -200-40\sqrt{5533} by 216.

$$x=\frac{-5\sqrt{5533}-25}{27}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-25+5\sqrt{5533}}{27} for x_{1} and \frac{-25-5\sqrt{5533}}{27} for x_{2}.

$$108x^{2}+200x-20400=108\left(x-\frac{5\sqrt{5533}-25}{27}\right)\left(x-\frac{-5\sqrt{5533}-25}{27}\right)$$

Evaluate

$$108x^{2}+200x-20400$$