Final answer:
To simplify the equation t² + 10t - 2000, we can use the quadratic formula to find the solutions. The quadratic formula is t = (-b ± sqrt(b² - 4ac)) / (2a). By substituting the values of a, b, and c into the formula, we can solve for t and get the solutions as t = 40 and t = -50.
Step-by-step explanation:
To simplify the equation t² + 10t - 2000, we can use the quadratic formula. The quadratic formula is used to find the solutions to quadratic equations in the form ax² + bx + c = 0. In this equation, a = 1, b = 10, and c = -2000.
The quadratic formula is given by:
t = (-b ± sqrt(b² - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get:
t = (-10 ± sqrt((10)² - 4(1)(-2000))) / (2(1))
Simplifying inside the square root:
t = (-10 ± sqrt(100 + 8000)) / 2
t = (-10 ± sqrt(8100)) / 2
t = (-10 ± 90) / 2
Now we have two possible values for t:
t = (-10 + 90) / 2 = 80 / 2 = 40
t = (-10 - 90) / 2 = -100 / 2 = -50
Therefore, the solutions to the equation t² + 10t - 2000 = 0 are t = 40 and t = -50.