I'm at 11s^2 - 6000s - 27500. Could someone show me the steps of using the quadratic formula to find s?

Answer 1

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.