1 SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

2 Completing the square If you expand the expressions (x + b)2 and (x – b)2 you should obtain the results: and Rearranging these gives you the following important results: This is known as completing the square.

3 1 Complete the square for the expression x2 − 8x.check:

4 2 Complete the square for the expression x2 + 6x.check:

5 3 Complete the square for the expression x2 − 12x.check:

6 4 Complete the square for the expression x2 + 5x.check:

7 5 Complete the square for the expression x2 + 4x + 12.check:

8 6 Complete the square for the expression x2 − 8x − 5.check:

9 You can solve quadratic equations by completing the square.

10 1 Solve the equation x2 − 8x − 5 = 0.add 5 to both sides complete the square add 16 to both sides square root add 4 to both sides

11 2 Solve the equation x2 + 10x − 7 = 0.add 7 to both sides complete the square add 25 to both sides square root take 5 from both sides