INVESTIGATION: SOLVING BY COMPLETING THE SQUARE There are different algebraic methods to solving a quadratic equation. Solving by factoring or by taking the square root are techniques that only work for special quadratic equations. In this investigation, you will develop a method that will solve any quadratic equation. 1. Solve each of the following equations. a. x2 = 9 b. x2 + 12 = 21 C. (x + 4) = 49 2. Now consider the equation x2 + 6x =4. A student attempted to solve the equation using similar reasoning used when solving the equations above. Analyze the student work and justify each step. x2 + 6x = 4 (i) Given x2 =4- 6x (ii) x =+ V4 - 6x (iii) Explain why the process used was effective in finding a numerical solution for the equations in problem set 1 and not effective in the case of x2 + 6x = 4. When the equation has the form of (x + a) or (x - a) equal to a numerical value then it is effective to take the square root to find a solution. The strategy is to rewrite the quadratic expression into the form by using the process of completing the square.3. The student tried again to solve the equation x2 + 6x = 4. This time using the process of completing the square. Analyze the work and justify each step. x2 + 6x = 4 (i) Given x2 + 6x - 4=0 (ii) (x2 + 6x+ 9) - 4-9=0 (x+ 3)2- 13= 0 (x + 3)2 = 13 x+3 = +V13 x= -3+ V134. Solve each of the following using the process of completing the square. a. x2 + 6x = 1 b. x2 + 14x = 38 C. x2 - 4x - 12 = 0 d. x2 - 12x + 15 =-8 e. x2 - 4x - 91 = 7 f. x2 = 18x + 40 g. 2x2 + 8x + 6=0 h. 3x2 - 30x =54 i. 3x2 - 20x + 10 = 16x - 13