Final answer:
To find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution, we use the quadratic formula to solve the equation and determine the roots. The largest interval is [-0.025, 0.025].
Step-by-step explanation:
To find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution, we can use the quadratic equation form ax^2 + bx + c = 0. In this case, the equation is x^2 + 0.00088x - 0.000484 = 0. We can solve this equation to find the roots using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a.
Using the formula, we substitute a = 1, b = 0.00088, and c = -0.000484. Calculating the roots, we find two possible values for x: x ≈ -0.025 and x ≈ 0.025.
Since x = 0 lies between these two values, the largest interval which includes x = 0 and has a unique solution is [-0.025, 0.025] in interval notation.