Final answer:
To solve the quadratic equation -16t^2 + 1600 = 0, rewrite it in standard form and use the quadratic formula to find t as 10 and -10, with the positive solution typically being the physically relevant one in context.
Step-by-step explanation:
To solve the quadratic equation -16t^2 + 1600 = 0 using the quadratic formula, we must first write the equation in the standard form, at^2 + bt + c = 0. For this equation, a = -16, b = 0, and c = 1600. The quadratic formula is -b ± √b^2 - 4ac / (2a).
Applying the quadratic formula:
- Calculate the discriminant: b^2 - 4ac = 0^2 - 4*(-16)*1600 = 102400.
- Compute the square root of the discriminant: √102400 = 320.
- Find the two solutions: t = -b ± √b^2 - 4ac / (2a) which simplifies to t = 0 ± 320 / (-32) = ± -10.
Therefore, the two solutions for t are t = 10 and t = -10. However, since t typically represents time, the negative value may not be applicable in a real-world context, and we would take t = 10 as the physical solution.