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Revision of What makes some equations so much easier to solve than others? from Tue, 16/12/2008 - 21:34

Quick description

Solving an equation can frequently be thought of as determining x given that f(x)=y, for some function f and some number y. For example, we might want to find x when (3x+5)^2=12, or when x^2+2x=8. If you think about these two examples, you will see that the first is much easier than the second. One sign that it is easier is that you can work out (3x+5)^2 on a calculator using no memory and inputting x only once: after putting x in, all you have to do is multiply it by 3, add 5, and square it. (This assumes your calculator has an x^2 button.)

Example 1

Suppose you are asked to solve the equation (3x+5)^2=12. It is rather easy to do: