2. X 2 + 2 = 11 X 2 = 9 X = 3 Check: X 2 + 2 = 3 x 3 +2 = 11 We can solve this equation by:

3. X 2 + 2 = 15 X 2 + 2 = 15 This is a method where we substitute different values for x until we get as close as we can to the answer, usually one decimal place Look at this equation: We can solve this in a similar way but for this type we are often asked to use trial and improvement

4. Using trial and improvement show that the equation X 2 + 2 = 15 has a solution between 3 and 4 The first thing we do is set up a table of values

5. Guess X 2 + 2 = 15 Comment In this column we write our guess or estimate Write the equation here Is the answer too big or too small?

6. Guess X 2 + 2 = 15 Comment 311 Too small 418 Too big 3.514.25Too small Try a value half- way between 3 and 4 Too small 3.614.96 3.715.69Too big To decide if the solution is closer to 3.6 or 3.7, try the middle value 3.65 15.3225 Too big The solution is between 3.6 and 3.7 we cannot just guess which is closer Always write down all the digits on your calculator

7. We only need the answer correct to one decimal place We only need the answer correct to one decimal place X = 3.65 was too big. X = 3.65 was too big. So your next guess would be smaller So your next guess would be smaller So you could try 3.64 or 3.63 So you could try 3.64 or 3.63 All these are 3.6 correct to 1 decimal place All these are 3.6 correct to 1 decimal place 3.6 3.65 3.7 So correct to one decimal place x would equal 3.6

8. Using trial and improvement show that the equation X 3 + 2x = 7 has a solution between 1 and 2 The first thing we do is set up a table of values

9. Guess X 3 + 2x = 7 Comment In this column we write our guess or estimate Write the equation here Is the answer too big or too small?

10. Guess X 3 + 2x= 7 Comment 13 Too small 212 Too big 1.56.375Too small Try the value half- way between 1 and 2 Too big 1.6 7.296 1.556.823875Too small To decide if the solution is closer to 1.5 or 1.6, try the middle value 1.55 The solution is between 1.5 and 1.6 remember we cannot just guess which is closer

11. We only need the answer correct to one decimal place We only need the answer correct to one decimal place X = 1.55 was too small. X = 1.55 was too small. So your next guess would be bigger So your next guess would be bigger You could try 1.56 or 1.57 You could try 1.56 or 1.57 All these would be 1.6 correct to 1 decimal place All these would be 1.6 correct to 1 decimal place 1.5 1.55 1.6 So correct to one decimal place x would equal 1.6

12. Using trial and improvement show that the equation X 3 + x = 105 has a solution between 4 and 5 Set up a table of values

13. Guess X 3 + x = 105 Comment

14. Guess Comment 468 Too small 5130 Too big 4.595.625Too small Try the value half- way between 4 and 5 Too small 4.6101.936 4.7108.523Too big To decide if the solution is closer to 4.6 or 4.7, try the middle value 4.65 105.194625 Too big The solution is between 4.6 and 4.7. Remember, we cannot just guess which is closer

15. We only need the answer correct to one decimal place We only need the answer correct to one decimal place X = 4.65 was too big. X = 4.65 was too big. So your next guess would be smaller So your next guess would be smaller You could try 4.64 or 4.63 You could try 4.64 or 4.63 All these would be 4.6 correct to 1 decimal place All these would be 4.6 correct to 1 decimal place 4.6 4.65 4.7 So correct to one decimal place x would equal 4.6

16. Using trial and improvement show that the equation 3X 2 - 4x = 18 has a solution between 3 and 4 Set up your table of values

17. Guess 3X 2 - 4x = 18 Comment

18. Guess Comment 315 Too small 432 Too big 3.522.75Too big Try the value half- way between 3 and 4 Too big 3.4 21.08 3.319.47Too big To decide if the solution is closer to 3.2 or 3.3, try the middle value 3.25 The solution is between 3.2 and 3.3 remember, we cannot just guess which is closer 3.217.92Too small 3.25 18.6875 Too big Remember to write down all the digits on your calculator

19. We only need the answer correct to one decimal place We only need the answer correct to one decimal place X = 3.25 was too big. X = 3.25 was too big. So your next guess would be smaller So your next guess would be smaller So you could try 3.24 or 3.23 So you could try 3.24 or 3.23 All these would be 3.2 correct to 1 decimal place All these would be 3.2 correct to 1 decimal place 3.2 3.25 3.3 So correct to one decimal place x would equal 3.2