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