Solve -80x^2+26x+2

$$-80 { x }^{ 2 } +26x+2$$

Factor

$$-80\left(x-\frac{13-\sqrt{329}}{80}\right)\left(x-\frac{\sqrt{329}+13}{80}\right)$$

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.

$$-80x^{2}+26x+2=0$$

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.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-80\right)\times 2}}{2\left(-80\right)}$$

Square 26.

$$x=\frac{-26±\sqrt{676-4\left(-80\right)\times 2}}{2\left(-80\right)}$$

Multiply -4 times -80.

$$x=\frac{-26±\sqrt{676+320\times 2}}{2\left(-80\right)}$$

Multiply 320 times 2.

$$x=\frac{-26±\sqrt{676+640}}{2\left(-80\right)}$$

Add 676 to 640.

$$x=\frac{-26±\sqrt{1316}}{2\left(-80\right)}$$

Take the square root of 1316.

$$x=\frac{-26±2\sqrt{329}}{2\left(-80\right)}$$

Multiply 2 times -80.

$$x=\frac{-26±2\sqrt{329}}{-160}$$

Now solve the equation x=\frac{-26±2\sqrt{329}}{-160} when ± is plus. Add -26 to 2\sqrt{329}.

$$x=\frac{2\sqrt{329}-26}{-160}$$

Divide -26+2\sqrt{329} by -160.

$$x=\frac{13-\sqrt{329}}{80}$$

Now solve the equation x=\frac{-26±2\sqrt{329}}{-160} when ± is minus. Subtract 2\sqrt{329} from -26.

$$x=\frac{-2\sqrt{329}-26}{-160}$$

Divide -26-2\sqrt{329} by -160.

$$x=\frac{\sqrt{329}+13}{80}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{13-\sqrt{329}}{80} for x_{1} and \frac{13+\sqrt{329}}{80} for x_{2}.

$$-80x^{2}+26x+2=-80\left(x-\frac{13-\sqrt{329}}{80}\right)\left(x-\frac{\sqrt{329}+13}{80}\right)$$

Evaluate

$$2+26x-80x^{2}$$