Solve y^2-208y-26700

$${ y }^{ 2 } -208y-26700$$

Factor

$$\left(y-\left(104-2\sqrt{9379}\right)\right)\left(y-\left(2\sqrt{9379}+104\right)\right)$$

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.

$$y^{2}-208y-26700=0$$

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.

$$y=\frac{-\left(-208\right)±\sqrt{\left(-208\right)^{2}-4\left(-26700\right)}}{2}$$

Square -208.

$$y=\frac{-\left(-208\right)±\sqrt{43264-4\left(-26700\right)}}{2}$$

Multiply -4 times -26700.

$$y=\frac{-\left(-208\right)±\sqrt{43264+106800}}{2}$$

Add 43264 to 106800.

$$y=\frac{-\left(-208\right)±\sqrt{150064}}{2}$$

Take the square root of 150064.

$$y=\frac{-\left(-208\right)±4\sqrt{9379}}{2}$$

The opposite of -208 is 208.

$$y=\frac{208±4\sqrt{9379}}{2}$$

Now solve the equation y=\frac{208±4\sqrt{9379}}{2} when ± is plus. Add 208 to 4\sqrt{9379}.

$$y=\frac{4\sqrt{9379}+208}{2}$$

Divide 208+4\sqrt{9379} by 2.

$$y=2\sqrt{9379}+104$$

Now solve the equation y=\frac{208±4\sqrt{9379}}{2} when ± is minus. Subtract 4\sqrt{9379} from 208.

$$y=\frac{208-4\sqrt{9379}}{2}$$

Divide 208-4\sqrt{9379} by 2.

$$y=104-2\sqrt{9379}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 104+2\sqrt{9379} for x_{1} and 104-2\sqrt{9379} for x_{2}.

$$y^{2}-208y-26700=\left(y-\left(2\sqrt{9379}+104\right)\right)\left(y-\left(104-2\sqrt{9379}\right)\right)$$

Evaluate

$$y^{2}-208y-26700$$