1. Equations Objectives for today’s lesson :
Using Trial & Improvement to estimate solutions to equations

2. Trial & Improvement
In some equations, it is very difficult to find the value of x.
We can find an estimate for x using ‘Trial & Improvement’

3. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion

4. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1

5. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1 10
110
x > 10

6. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1 10
110
x > 10 30
930
too high
10 < x < 30

7. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1 10
110
x > 10 30
930
too high
10 < x < 30 15
240
15 < x < 30

8. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1 10
110
x > 10 30
930
too high
10 < x < 30 15
240
15 < x < 30 22
504
15 < x < 22

9. Trial & Improvement Example Solve x2 + x = 420 Trial Value x2 + x
Comment
Conclusion 1 2
too low
x > 1 10
110
x > 10 30
930
too high
10 < x < 30 15
240
15 < x < 30 22
504
15 < x < 22 20
420
CORRECT

10. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1

11. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5

12. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5 2 7
2 < x < 5

13. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5 2 7
2 < x < 5
2.5
14.625
2 < x < 2.5

14. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5 2 7
2 < x < 5
2.5
14.625
2 < x < 2.5
2.2
9.648
2.2 < x < 2.5

15. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5 2 7
2 < x < 5
2.5
14.625
2 < x < 2.5
2.2
9.648
2.2 < x < 2.5
2.3
11.167
2.2 < x < 2.3

16. Trial & Improvement Try Solve x3 - 1 = 10 Trial Value x3 – 1 Comment
Conclusion 1
Too low
x > 1 5
124
Too high
1 < x < 5 2 7
2 < x < 5
2.5
14.625
2 < x < 2.5
2.2
9.648
2.2 < x < 2.5
2.3
11.167
2.2 < x < 2.3

17. Trial & Improvement
Try these questions :
Page 199 Q2
Extension Q4