1. A student tries to solve 𝑥 2 +3𝑥=50 as follows
Discuss: What has the student done to get from the equation to line 1 and from line 1 to line 2?
Why is this not the answer?

2. A student tries to solve 𝑥 2 +3𝑥=50 as follows
𝑥 2 =50−3𝑥 𝑥= 50−3𝑥
The solution will be a value of 𝑥 that when substituted into the equation gives the value of 𝑥 used

3. To speed this process up we can use the ANS button as follows…
Let’s start with 0… 𝑥 1 =0
𝑥 2 = 50−3×0 =7.071…
𝑥 3 = 50−3×7.071… =5.365…
𝑥 4 = 50−3×5.365… =5.823…
To speed this process up we can use the ANS button as follows…
𝑥 4 = 50−3×𝐴𝑁𝑆 =5.704…
𝑥 5 = 50−3×𝐴𝑁𝑆 =5.735…
𝑥 6 = 50−3×𝐴𝑁𝑆 =5.727…
𝑥 7 = 50−3×𝐴𝑁𝑆 =5.729…
What do you notice?

4. The values of 𝑥 𝑛+1 is getting closer the value of 𝑥 𝑛
𝑥 4 = 50−3×𝐴𝑁𝑆 =5.704…
𝑥 5 = 50−3×𝐴𝑁𝑆 =5.735…
𝑥 6 = 50−3×𝐴𝑁𝑆 =5.727…
𝑥 7 = 50−3×𝐴𝑁𝑆 =5.729…
The values of 𝑥 𝑛+1 is getting closer the value of 𝑥 𝑛
A solution is 𝒙=𝟓.𝟕𝟑 𝟐 𝒅𝒑

5. Javed is solving a problem and needs to know the solutions of the equation 5𝑥 2 −3𝑥−4=0. He plans to use an iteration.
Javed decides to use the iterative formula 𝑥 𝑛+1 = 3 𝑥 𝑛 +4 5 Using 𝑥 0 =5 Find a solution to Javed’s equation to 2 decimal places.
Whiteboards

6. Javed decides to use the iterative formula 𝑥 𝑛+1 = 3 𝑥 𝑛 +4 5 Using 𝑥 0 =5 Find a solution to Javed’s equation to 2 decimal places.
𝑥 1 = 3× =
Whiteboards
𝑥 2 = 3×𝐴𝑁𝑆+4 5 = …

7. In your books: 1. 2. 3.

8. Challenge Acknowledgements:
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