Final answer:
To solve the given equation using the quadratic formula, follow these steps: identify the values of a, b, and c, substitute the values into the quadratic formula, calculate the discriminant, and substitute the values back into the formula to find the roots.
Step-by-step explanation:
To solve the equation 5. Use the quadratic formula to solve for t. (a) Rearrange the equation to get 0 on one side of the equation. t² + 10t - 200 = 0 using the quadratic formula, we can follow the steps:
- Identify the values of a, b, and c in the equation. In this case, a=1, b=10, and c=-200.
- Substitute the values of a, b, and c into the quadratic formula: t = (-b ± √(b² - 4ac)) / (2a)
- Calculate the discriminant (b² - 4ac) and determine the nature of the roots. If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root; if negative, there are two complex roots.
- Substitute the values of a, b, and c, as well as the discriminant, into the quadratic formula and simplify to find the values of t.
By following these steps, you can solve the equation for t, which in this case will yield two values.