Solving a quadratic equation of the form, ax2 + bx + c = 0, can be accomplished by using a square root property.
| Square Root Property | If a and b are complex numbers, and if a2 = b2 then a = b or a = -b. |
Example 1: Solve x2 = 7
| Solution | |
| x2 = 7 | Given |
| x2 = (71/2)2 | 7 = (71/2)2, Substitution |
| x = 71/2 or x = -71/2 | Square Root Property |
Example 2: Solve (2x - 5)2 = 18
| Solution | |
| (2x - 5)2 = 18 | Given |
| (2x - 5)2 = (181/2)2 | 18 = (181/2)2, Substitution |
| 2x - 5 = 181/2 or 2x - 5 = -181/2 | Square Root Property |
| x = (5 + 181/2) / 2 or x = (5 - 181/2) / 2 | Solve for x |
Example 3: Solve 2x2 - 4x -5 = 0
| Solution | |
| 2x2 - 4x -5 = 0 | Given |
| x2 - 2x - 5/2 = 0 | Divide both sides by a |
| x2 - 2x = 5/2 | Variable terms on left |
| x2 - 2x + 1 = 5/2 + 1 | Add (b/2)2 to both sides |
| (x - 1)2 = ((7/2)1/2)2 | Complete the square |
| x - 1 = (7/2)1/2 or x - 1 = - (7/2)1/2 | Square Root Property |
| x = 1 + (7/2)1/2 or x = 1 - (7/2)1/2 | Solve for x |