Final answer:
The expression that has the solution equal to 14.5 is a quadratic equation where the constants are a = 4.90, b = 14.3, and c = -20.0. Using the quadratic formula, we can find the solutions as x = 14.5 or x = -5.5.
Step-by-step explanation:
This expression 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. Its solutions are given by the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values, we have:
x = (-14.3 ± √((14.3)² - 4(4.90)(-20.0))) / (2(4.90))
Simplifying further, we get:
x = (-14.3 ± √(204.49 + 392)) / 9.8
x = (-14.3 ± √(596.49)) / 9.8
x = (-14.3 ± 24.40) / 9.8
Therefore, the solutions of the quadratic equation are:
x = (-14.3 + 24.40) / 9.8 or x = (-14.3 - 24.40) / 9.8
Simplifying further, we have:
x = 14.5 or x = -5.5