When a quadratic expression is a perfect square, its discriminant (\(b^2 - 4ac\)) must equal zero. Set \(b^2 - 4ac = 0\) 4x\(^2\) - 8x + k Let what must be added be k Comparing \(b^2 - 4ac = 0\) with 4x\(^2\) - 8x + k a = 4, b = -8, c = k \(b^2\) = 4ac (-8)\(^2\) = 4 . 4 x k 64 = 16k k = \(\frac{64}{16}\) k = 4