Final answer:
To solve the quadratic equation t² + 10t - 200 = 0, we identify a = 1, b = 10, and c = -200 and apply the quadratic formula to find the solutions for t.
Step-by-step explanation:
To solve the quadratic equation t² + 10t - 200 = 0 using the quadratic formula, we must identify the coefficients in the equation and apply the formula.
For any quadratic equation of the form at² + bt + c = 0, the quadratic formula is given by:
t = (-b ± √(b² - 4ac)) / (2a)
In this case, the coefficients are a = 1.00, b = 10.0, and c = -200. Plug these values into the quadratic formula to find the solutions for t:
t = (-10.0 ± √((10.0)² - 4(1.00)(-200))) / (2(1.00))
Simplify the expression under the radical and solve for t to get the two possible solutions for the equation.