Solving Quadratic Equations by Completing the Square Before we learn how to solve quadratic equations by completing the square, let’s go over how to solve the problem given to you two weeks ago. Solution to Problem from Two Weeks Ago Two weeks ago we went over how to solve simple quadratic equations using the square root property. To review that material click the following link: The Square Root Property on the SAT I also promised to provide a solution to the following question: (x – 3)2 = 2 What is the solution set of the above equation? (A) {1, 5} (B) {3 + √2} (C) {3 – √2, 3 + √2} (D) The equation has no solutions. Solution: When we apply the square root property we get x – 3 = ±√2. We then add 3 to each side of this last equation to get the two solutions x = 3±√2. This is choice (C). Completing the Square Before we solve a quadratic equation by completing the square you may want to review the procedure of completing the square itself. You can find a detailed explanation of that procedure here: Completing the Square on the SAT Solving Quadratic Equations by Completing the Square A quadratic equation has the form ax2 + bx + c = 0. Let’s use an example to show how to solve such an equation by completing the square. Example: In the quadratic equation x2 – 2x – 15 = 0, find the positive solution for x. Solution by completing the square: We first add 15 to each side of the given equation to get x2 – 2x = 15. We now take half of –2, which is –1, and square this number to get 1. We then add 1 to each side of the equation to get x2 – 2x + 1 = 16. This is equivalent to (x – 1)2 = 16. We now apply the square root property to get x – 1 = ±4. So x = 1 ± 4. This yields the two solutions 1 + 4 = 5, and 1 – 4 = –3. Since we want the positive solution for x, the answer is 5. If you liked this article, please share it with your Facebook friends: Comments comments