Warm-Up

Lesson 11.3: Finding Complex Solutions to Quadratic Equations In the past when solving quadratic equations, we were only interested in “real” solutions. Now we want to consider all solutions, real number and non-real number solutions.

Completing the Square Solve x2 – 4x = -5 by completing the square. x2 – 4x + 4 = -5 + 4 add 4 to both sides (x – 2)2 = -1 factor into a perfect square x – 2 = take square root of both sides x = 2 ± i add 2 to both sides so x = 2 + i or x = 2 – i are the two solutions

Another Example Solve -2x2 + 6x – 10 = 0 by completing the square. -2x2 + 6x = 10 add 10 to both sides x2 – 3x = -5 divide both sides by -2 x2 – 3x + = -5 + add to both sides (x – )2 = factor into a perfect square x – = take square root of both sides x = add to both sides So solutions are

Using Quadratic Formula Solve x2 – 4x + 20 = 0 using Quadratic Formula. a = 1, b = -4, c = 20