Final answer:
To solve the given equation for 't', we use the quadratic formula. For the equation t² + 10t - 2000 = 0, 't' has two possible solutions, which are t = 40 and t = -50 after applying the quadratic formula with 'a' as 1, 'b' as 10 and 'c' as -2000.
Step-by-step explanation:
To solve the equation rm=t²-mt for t, we first move everything to one side to set the equation to zero. Doing so, we obtain a quadratic equation. The quadratic formula, which is t = (-b ± sqrt(b² - 4ac))/(2a), can then be used to solve for t.
In the second example, we see the equation t² + 10t - 2000 = 0. Applying the quadratic formula, we identify a = 1, b = 10, and c = -2000. Substituting these values, we get:
t = (-10 ± sqrt(10² - 4(1)(-2000)))/(2(1))
t = (-10 ± sqrt(100 + 8000))/2
t = (-10 ± sqrt(8100))/2
t = (-10 ± 90)/2
Yielding two possible solutions for t:
- t = (-10 + 90)/2 = 80/2 = 40
- t = (-10 - 90)/2 = -100/2 = -50 (which might be rejected depending on the context, because time is usually positive)