Worked Example
The following is an illustration of how equations may be solved by means of trial and improvement.
Solve x2 + 3x = 9.
In this method, we try values of x in the equation, for example x = 2.
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22 + 3 x 2 = 10 |
(too large) |
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| Next we could try x = 1. |
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12 + 3 x 1 = 4 |
(too small) |
Then we could try a value halfway between 1 and 2 such as x = 1,5.
Using a calculator: 1,52 + 3 x 1,5 = 6,75
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(too small) |
Try x = 1,8. |
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1,82 + 3 x 1,8 = 8,64 |
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(too small) |
Try x = 1,9. |
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1,92 + 3 x 1,9 = 9,31 |
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(too large) |
If we are asked for an answer to one decimal place we must try x = 1,85.
1,852 + 3 x 1,85 = 8,9725 |
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(too small) |
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So x = 1,9 |
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(one decimal place) |
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