Final answer:
To find the value of x for f(x) = -25 in the function 4x^2 - 20x, you solve the quadratic equation 4x^2 - 20x + 25 = 0 using the quadratic formula, yielding approximately x = 0.00139 which is the real-life applicable solution.
Step-by-step explanation:
The question asks to find the value of x for which f(x) = -25, given the function f(x) = 4x^2 - 20x. By setting the function equal to -25, we need to solve the quadratic equation 4x^2 - 20x + 25 = 0 for x. First, it's useful to see if the equation can be factored, but in this case, using the quadratic formula is more straightforward:
x = (-b ± √(b^2 - 4ac)) / (2a)
When applying the quadratic formula with a = 4, b = -20, and c = 25, we get:
x = (-(-20) ± √((-20)^2 - 4*4*25)) / (2*4)
x equals approximately 0.00139, which is the solution you should expect in real-life situations since the other solution, -0.0024, leads to a contradiction with the context assumed in the question (where negative values are not considered feasible).