Final answer:
To solve the quadratic equation t² + 10t - 2000 = 0, the quadratic formula t = [-b ± sqrt(b² - 4ac)]/(2a) is applied, yielding two solutions: t = 40 and t = -50.
Step-by-step explanation:
To solve the quadratic equation t² + 10t - 2000 = 0 for t, we will use the quadratic formula. This formula is used to find the solutions for the equation of the form at² + bt + c = 0. The quadratic formula is given by:
t = ∓[-b ± sqrt(b² - 4ac)]/(2a)
For the given equation, a = 1, b = 10, and c = -2000. Substituting these values into the quadratic formula:
t = [-10 ± sqrt(10² - 4(1)(-2000))]/(2 * 1)
t = [-10 ± sqrt(100 + 8000)]/2
t = [-10 ± sqrt(8100)]/2
t = [-10 ± 90]/2
Now, we break it down into two possible solutions:
t = (-10 + 90)/2 = 40
or
t = (-10 - 90)/2 = -50
So, the solutions for the equation t² + 10t - 2000 = 0 are t = 40 and t = -50.