Final answer:
The student is dealing with a quadratic equation, and the solution for the variable is found using the quadratic formula based on given values for a, b, and c. Examples are provided with different sets of a, b, and c to demonstrate the calculation process.
Step-by-step explanation:
It seems like the student is asking how to solve a quadratic equation when given specific values for the constants a, b, and c. Let's define the quadratic equation as at² + bt + c = 0. The solution for t is found using the quadratic formula, which is t = (-b ± √(b² - 4ac)) / (2a).
For the example with a = 3, b = 13, and c = -10, the solution would be found as follows:
- Calculate the discriminant (√(b² - 4ac)) which is √((13)² - 4 × 3 × (-10)).
- Find two solutions using the quadratic formula, which gives t = (-13 ± √(discriminant)) / (2 × 3).
- Finally, you would end up with two potential solutions for t.
For the case of a = 1.00, b = 10.0, and c = -200, the quadratic formula will yield two different solutions for t as well.