Solving the Equation u^4 - 6u^2 + 25 = 0: A Step-by-Step Guide

To solve the equation u^4 - 6u^2 + 25 = 0, we can use the quadratic formula. \n\nLet's substitute u^2 as x: x^2 - 6x + 25 = 0. \n\nUsing the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = -6, and c = 25. \n\nSubstituting these values into the formula, we have x = (-(-6) ± √((-6)^2 - 4(1)(25))) / (2(1)). \n\nSimplifying, x = (6 ± √(36 - 100)) / 2. \n\nx = (6 ± √(-64)) / 2. \n\nSince the square root of a negative number is not a real number, there are no real solutions to the equation u^4 - 6u^2 + 25 = 0.