Solve 80x^2-399x-358

$$80 { x }^{ 2 } -399x-358$$

Factor

$$80\left(x-\frac{399-\sqrt{273761}}{160}\right)\left(x-\frac{\sqrt{273761}+399}{160}\right)$$

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.

$$80x^{2}-399x-358=0$$

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.

$$x=\frac{-\left(-399\right)±\sqrt{\left(-399\right)^{2}-4\times 80\left(-358\right)}}{2\times 80}$$

Square -399.

$$x=\frac{-\left(-399\right)±\sqrt{159201-4\times 80\left(-358\right)}}{2\times 80}$$

Multiply -4 times 80.

$$x=\frac{-\left(-399\right)±\sqrt{159201-320\left(-358\right)}}{2\times 80}$$

Multiply -320 times -358.

$$x=\frac{-\left(-399\right)±\sqrt{159201+114560}}{2\times 80}$$

Add 159201 to 114560.

$$x=\frac{-\left(-399\right)±\sqrt{273761}}{2\times 80}$$

The opposite of -399 is 399.

$$x=\frac{399±\sqrt{273761}}{2\times 80}$$

Multiply 2 times 80.

$$x=\frac{399±\sqrt{273761}}{160}$$

Now solve the equation x=\frac{399±\sqrt{273761}}{160} when ± is plus. Add 399 to \sqrt{273761}.

$$x=\frac{\sqrt{273761}+399}{160}$$

Now solve the equation x=\frac{399±\sqrt{273761}}{160} when ± is minus. Subtract \sqrt{273761} from 399.

$$x=\frac{399-\sqrt{273761}}{160}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{399+\sqrt{273761}}{160} for x_{1} and \frac{399-\sqrt{273761}}{160} for x_{2}.

$$80x^{2}-399x-358=80\left(x-\frac{\sqrt{273761}+399}{160}\right)\left(x-\frac{399-\sqrt{273761}}{160}\right)$$

Evaluate

$$80x^{2}-399x-358$$