Solve 18x^2+600-230x

$$18 { x }^{ 2 } +600-230x$$

Factor

$$18\left(x-\frac{115-5\sqrt{97}}{18}\right)\left(x-\frac{5\sqrt{97}+115}{18}\right)$$

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.

$$18x^{2}-230x+600=0$$

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.

$$x=\frac{-\left(-230\right)±\sqrt{\left(-230\right)^{2}-4\times 18\times 600}}{2\times 18}$$

Square -230.

$$x=\frac{-\left(-230\right)±\sqrt{52900-4\times 18\times 600}}{2\times 18}$$

Multiply -4 times 18.

$$x=\frac{-\left(-230\right)±\sqrt{52900-72\times 600}}{2\times 18}$$

Multiply -72 times 600.

$$x=\frac{-\left(-230\right)±\sqrt{52900-43200}}{2\times 18}$$

Add 52900 to -43200.

$$x=\frac{-\left(-230\right)±\sqrt{9700}}{2\times 18}$$

Take the square root of 9700.

$$x=\frac{-\left(-230\right)±10\sqrt{97}}{2\times 18}$$

The opposite of -230 is 230.

$$x=\frac{230±10\sqrt{97}}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{230±10\sqrt{97}}{36}$$

Now solve the equation x=\frac{230±10\sqrt{97}}{36} when ± is plus. Add 230 to 10\sqrt{97}.

$$x=\frac{10\sqrt{97}+230}{36}$$

Divide 230+10\sqrt{97} by 36.

$$x=\frac{5\sqrt{97}+115}{18}$$

Now solve the equation x=\frac{230±10\sqrt{97}}{36} when ± is minus. Subtract 10\sqrt{97} from 230.

$$x=\frac{230-10\sqrt{97}}{36}$$

Divide 230-10\sqrt{97} by 36.

$$x=\frac{115-5\sqrt{97}}{18}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{115+5\sqrt{97}}{18} for x_{1} and \frac{115-5\sqrt{97}}{18} for x_{2}.

$$18x^{2}-230x+600=18\left(x-\frac{5\sqrt{97}+115}{18}\right)\left(x-\frac{115-5\sqrt{97}}{18}\right)$$

Evaluate

$$18x^{2}-230x+600$$