I'm at 11s^2 - 6000s - 27500. Could someone show me the steps of using the quadratic formula to find s?
Sure! The quadratic formula is used to find the solutions for any quadratic equation in the form of ax^2 + bx + c = 0. In this case, we have the equation 11s^2 - 6000s - 27500 = 0, where a = 11, b = -6000, and c = -27500.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Now let's substitute the values into the formula:
s = (-(-6000) ± √((-6000)^2 - 4*11*(-27500))) / (2*11)
Simplifying further:
s = (6000 ± √(36000000 + 1210000)) / 22
s = (6000 ± √(37210000)) / 22
s = (6000 ± √(6100^2)) / 22
s = (6000 ± 6100) / 22
Now, we have two possible solutions:
s1 = (6000 + 6100) / 22
s1 = 12100 / 22
s1 = 550
s2 = (6000 - 6100) / 22
s2 = -100 / 22
s2 ≈ -4.55
Therefore, the solutions for s are approximately s = 550 and s ≈ -4.55.