1. First consider a geometric illustration of completing the square for
x2 + 2x

2. 1 square unit
x square units x
Area = x2
+ x
+ x
= x2 + 2x

3. x
Complete the square by clicking ‘Enter’ once.
1 square unit
x square units

4. x + 1
Area = (x + 1)2
1 square unit
x square units

5. x2 + 2x + 1 = (x + 1)2 x2 + 2x 1 square unit x square units (x + 1)2 1

6. Consider completing the square for
x2 + 3x

7. Area = x2
+ x
+ x
+ x
= x2 + 3x x
1 square unit
x square units

8. x + 1.5 x
1 square unit
x square units
0.5x square units

9. x + 1.5 x
1.5
2.25
1 square unit
x square units
0.5x square units

10. Area = x2 + 3x
x + 1.5
Area = (x + 1.5)2 x
1.5
1 square unit
x square units
0.5x square units

11. x2 + 3x
2.25
(x + 1.5)2 + =
x2 + 3x = (x + 1.5)2