15 mins
Trial and improvement
The purpose of trial and improvement is to narrow in on an answer.
I am going to use the equation 2x3+5=24
Find x to 1 decimal place
You start by drawing a table:
x
2x3+5=
h/l
You then make an educated guess as to what the value of x could be I am choosing 3
x
3
2x3+5=
59
h/l
H
As you can see by putting the value of x=3 in the equation the answer comes to 59
which is more than 24 so it is too high, I will chose a lower value of x (2)
x
3
2
2x3+5=
59
21
h/l
H
L
This time the answer comes out to 21 which is below 24 so I need a higher value of x
(2.5)
x
3
2
2.5
2x3+5=
59
21
36.25
h/l
H
L
H
This time the answer comes out above 24 so I need a lower value of x (2.2)
x
3
2
2.5
2x3+5=
59
21
36.25
h/l
H
L
H
2.2
26.296
H
This time the answer comes out above 24 so I need a lower value of x (2.1)
x
3
2
2.5
2.2
2.1
2x3+5=
59
21
36.25
26.296
23.522
h/l
H
L
H
H
L
You can now see the value of x is between 2.1 and 2.2 to get an answer to one
decimal place we need to find out whether the answer is above or below 2.15
x
3
2
2.5
2.2
2.1
2.15
2x3+5=
59
21
36.25
26.296
23.522
24.87675
h/l
H
L
H
H
L
H
As the answer comes out above 24 when x =2.15 we know the value of x must be
below 2.15 so the value of x to 1 decimal place is 2.1.
If you need to go to more decimal places you just continue with the table, each
‘guess’ will bring you closer to the actual value.