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Sometimes we must use trial and improvement to approximate the result of cubic equations.

Example

Solution

In order to tackle this question we must first construct a table:

This is where we will record the steps we have taken in order to find the solution. We know the answer lies between 3 and 4 so we will start by trying 3.5 (as shown in the table).

As the outcome was too small, we will now try a larger number: 3.7

The answer is still too small so we shall try 3.8

Now the answer is too large, but we also know that 3.7 is too small. As we are asked to give our answer correct to one decimal place, we must either choose 3.7 or 3.8. The way we decide is by using 3.75. If this is too big, then our answer will be 3.7. If it is too small, our answer will be 3.8.