Final answer:
The quadratic equation 4u² + 20u + 25 = 0 has a single solution for u, which is u = −(2.5), found by using the quadratic formula.
Step-by-step explanation:
To solve for u in the quadratic equation 4u² + 20u = -25, we first need to bring the equation to standard form, which is at² + bt + c = 0. We do this by adding 25 to both sides of the equation to get 4u² + 20u + 25 = 0. Next, we use the quadratic formula −b ± √(b² - 4ac) / (2a) to find the solutions for u.
First, we identify a = 4, b = 20, and c = 25. Plugging these values into the quadratic formula gives us:
u = −(20) ± √((20)² - 4·(4)·(25)) / (2·(4))
u = −(20) ± √(400 - 400) / 8
u = −(20) ± √(0) / 8
u = −(20) / 8
u = −(2.5)
Since the discriminant (b² - 4ac) is zero, there is only one real solution to the equation, which is u = −(2.5).