Final answer:
To simplify the given quadratic equation h(t) = -t(16t + 7), we can use the quadratic formula. Substituting the values for a, b, and c into the formula, we get two solutions for t: -0.88 and 4.18.
Step-by-step explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0. Its solutions are given by the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Let's substitute the values for a, b, and c into the formula:
t = (-(-14.3) ± √((-14.3)² - 4(4.90)(-20.0))) / (2(4.90))
Simplifying further, we get:
t = (14.3 ± √(204.49 + 392)) / 9.8
t = (14.3 ± √596.49) / 9.8
t = (14.3 ± 24.42) / 9.8
Therefore, the solutions to the quadratic equation are t = -0.88 and t = 4.18.