Form and solve equations such as x<sup>3</sup> + x = 12 using trial and improvement methods
Some equations are difficult to solve without advanced methods.
In those cases, it can still be possible to solve a linear or quadratic equation by using trial and improvement. In short, you try a number, any number, substitute it into the equation and see how closely the result matches the equation.
If the result is too big, then next time you try a smaller number. If it was too small, next time you try a bigger number.
This way, you can steadily get closer and closer to an accurate solution to the equation.
In a GCSE exam, you will usually be a given a start point, by being told, for example, and that the answer for the quadratic equation (or linear) has a solution somewhere between 3 and 4. You would then be expected to select 3.5 as your first attempt.
The second important thing to note, is that if you’re asked to find a solution to 1d.p., you will still be expected to try out values down to 2d.p. before giving your final answer.
For example, say you work out that the solution to an equation is between 3.7 and 3.8, although from your results it is possible to work out which is closer to the real solution, you will still be expected to test out 3.75 (the midway point) before declaring whether you think 3.7 or 3.8 is correct to 1 d.p.
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