Problem 1: Solve each quadratic equation by factoring. a. x2 - 4x +4 = 0 b. 6y' + 5y - 1 = 3 c. 212 = 15 - 7t Problem 2: Solve each quadratic equation by completing the square. a. x2 - 6: + 2= 0 b. 2t2 + 6t = 3 Problem 3: Consider the equation 3x2 - 4x -1 =0. Complete the following. a. Calculate the discriminant. b. Based on the discriminant, state if the solutions to the equation are real or (non-real) complex. c. State the number of solutions (real or (non-real) complex) to the equation. d. Use the quadratic formula to solve the equation. Simplify your answer fully, leave it in exact form. Problem 4: Consider the equation 5x2 - 4x + = =0. Complete the following. a. Calculate the discriminant. b. Based on the discriminant, state if the solutions to the equation are real or (non-real) complex. c. State the number of solutions (real or (non-real) complex) to the equation. d. Use the quadratic formula to solve the equation. Simplify your answer fully, leave it in exact form. Problem 5: A box with no top is to be constructed from a piece of cardboard whose length measures 15 inches more than its width. The box is formed by cutting squares that measure 5 inches on each side from the four corners and then folding the sides. W + 15 W a. Find a formula that measures the volume of the box as a function of w. b. If the volume of the box will be 270 in", what are the dimensions of the piece of cardboard? Do not round until the final answer. For the final answer round to the nearest hundredth as needed and include appropriate units