### Quick description

Solving an equation can frequently be thought of as determining given that , for some function and some number . For example, we might want to find when , or when . 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 on a calculator using no memory and inputting only once: after putting in, all you have to do is multiply it by 3, add 5, and square it. (This assumes your calculator has an button.)

### Example 1

Suppose you are asked to solve the equation . It is rather easy to do: taking square roots tells you that , subtracting 5 gives , and dividing by 3 gives .

Now suppose you are asked to solve the equation . It isn't nearly so easy, and you have to use the full theory of quadratic equations to solve it.

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