Final answer:
The value of p that makes the expression a perfect square is 25.
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)
To determine the value of p so that the expression 4X^2 + 20x + p is a perfect square, we need to set the discriminant (b² - 4ac) to zero. In this case, b² - 4ac = 0, so we have (20)² - 4(4)(p) = 0. Solving this equation, we find:
400 - 16p = 0
Simplifying, we get: 16p = 400
p = 400/16
p = 25