Final answer:
To solve the quadratic equation t² + 10t - 2000 = 0, we can use the quadratic formula. Rearrange the equation to get 0 on one side, then substitute the values into the quadratic formula to find the solutions. Discard the negative solution to obtain the final answer.
Step-by-step explanation:
To solve the equation t² + 10t - 2000 = 0 using the quadratic formula, we first need to rearrange the equation to get 0 on one side:
t² + 10t - 2000 = 0
Using the quadratic formula, t = (-b ± √(b² - 4ac)) / (2a), where a = 1, b = 10, and c = -2000, we can substitute these values into the formula:
t = (-10 ± √(10² - 4(1)(-2000))) / (2(1))
Simplifying the equation, we get t = (-10 ± √(100 + 8000)) / 2
Finally, t = (-10 ± √8100) / 2, which gives us the solutions t ≈ 43.08 and t ≈ -53.08. Since time cannot be negative in this context, we discard the negative solution and conclude that t ≈ 43.08.