The equation
x^2+ 3x = 94
has a solution between 8 and 9.
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
On the same line as your final answer you must write “to 1 decimal place".

Let's use a trial and improvement method to find this solution.

Step 1. Let's choose x = 8.5

Substituting into the equation:

Step 2. Let's choose x = 8.4

Substituting into the equation:

Step 3. Let's choose x = 8.3

Substituting into the equation:

Since the sign of the equation changes from positive to negative when evaluating from 8.4 to 8.3, then x = 8.3 seems to be a reasonable value. Finally, the solution to 1 decimal place is: