Final answer:
The solution to the equation t² + 10t - 200 = 0 using the quadratic formula is t = 10 seconds, as time cannot be negative in this context.
Step-by-step explanation:
To solve the quadratic equation t² + 10t - 200 = 0, you can use the quadratic formula. The general form of a quadratic equation is ax² + bx + c = 0, and the quadratic formula is t = (-b ± √(b² - 4ac))/(2a). In our case, a = 1, b = 10, and c = -200.
By substituting our values of a, b, and c into the quadratic formula, we get:
t = (-10 ± √((10)² - 4(1)(-200)))/(2(1))
t = (-10 ± √(100 + 800))/2
t = (-10 ± √(900))/2
t = (-10 ± 30)/2
This gives us two possible solutions for t:
- t = (-10 + 30)/2 = 20/2 = 10
- t = (-10 - 30)/2 = -40/2 = -20
Since time cannot be negative in this context, the solution to the equation is t = 10 seconds.