1. Table of Contents First, add (or subtract) to place the constant on the right side. Quadratic Equation: Solving by completing the square Example: Solve 3x 2 + 12x + 7 = 0. 3x 2 + 12x = - 7 Next, divide every term on both sides by a number chosen to make "1" the coefficient of the x 2. Next, take half of the x-term coefficient and square this. Then add this to both sides. Half of 4 is 2. Square this to get 4 so:

2. Table of Contents (x + half of the x-term coef.) 2. Note, the constant terms on the right can be combined now. Quadratic Equation: Solving by completing the square The trinomial on the left is a perfect square. It can be written in the form: Slide 2 Now solve by taking the square root of both sides.

3. Table of Contents Quadratic Equation: Solving by completing the square Slide 3 Try to solve 2x 2 – 6x = - 7 by completing the square. The solutions are (merged into a single fraction). Notes: The example on the preceding two slides resulted in two real solutions. Most textbooks would display the However, when the solutions are nonreal (as in one just tried) the solutions are usually written in the standard form of a complex number, a + bi. solutions as

4. Table of Contents Quadratic Equation: Solving by completing the square