Final answer:
To solve the quadratic equation -16t² + 32t + 46 = 0 using the quadratic formula, substitute the values of a, b, and c into the formula. Simplify the equation and calculate the values of t. The solutions are approximately t = 3.96 and t = -1.03.
Step-by-step explanation:
The given equation 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. To solve this equation using the quadratic formula, we substitute the values of a, b, and c into the formula:
t = (-b ± √(b² - 4ac)) / (2a)
Substituting the given values into the formula, we have:
t = (-(-14.3) ± √((-14.3)² - 4 * 4.90 * (-20.0))) / (2 * 4.90)
t = (14.3 ± √(204.49 + 392)) / 9.8
t = (14.3 ± √596.49) / 9.8
t = (14.3 ± 24.42) / 9.8
t = (14.3 + 24.42) / 9.8 or t = (14.3 - 24.42) / 9.8
t = 38.72 / 9.8 or t = -10.12 / 9.8
t ≈ 3.96 or t ≈ -1.03
The solutions to the equation are t ≈ 3.96 and t ≈ -1.03.