Question 1: Complete the square to solve x^2 + 6x + 5 = 0.

Answer: x = -1 or x = -5

Question 2: Solve 2x^2 - 8x + 6 = 0 by completing the square.

Answer: x = 1 ± √2

Question 3: Solve x^2 - 4x = 0 using the completing the square method.

Answer: x = 0 or x = 4

Question 1: A ball is thrown upwards, its height h (in meters) after t seconds is given by h = -4t^2 + 8t + 2. Use completing the square to find when the ball reaches its maximum height and what that height is.

Answer: Maximum height at t=1 second, height=6 meters.

Question 1: A farmer fences a rectangular area with a total length of fencing of 50 meters. If the length is 10 meters more than the width, find the dimensions of the rectangle using completing the square.

Answer: Width = 10 meters, Length = 20 meters.

Question 1: Solve 3x^2 + 12x + 7 = 0 by completing the square. Identify and correct any mistakes in the standard method.

Answer: x = -2 ± √(1/3)

Question 1: Complete the square for x^2 - 10x + 21.

Answer: x = 5 ± √4

Question 2: Explain why completing the square is a reliable method for solving quadratics, especially in comparison to factorization.

Answer: It always works regardless of whether the quadratic factors neatly and helps in understanding the vertex form.

Question 1: A student solves x^2 + 4x + 4 = 0 by completing the square and gets x = -2. Find the mistake and solve correctly.

Answer: Correct solution: x = -2, x = -2 (double root). No mistake, solution is correct.

Question 2: Solve 2x^2 + 8x + 6 = 0 by completing the square, but the student writes (x+2)^2 = 0. Identify the error and find the correct solutions.

Answer: Error: Incorrect expansion and addition of constants. Correct steps lead to x = -1 ± √2.