Answer
The number is 4 or 8
Explanation:
Let y be the number.
The square of g is written as y^2
12 times the number is written as 12y.
But from the question, we were told that The square of the number is smaller than 12 times the number by 32. This can be written as
12y — y^2 = 32
Rearranging the above equation, we obtain:
y^2 — 12y + 32 = 0
We can solve the above equation using factorization method by doing the following:
Multiply the first term(i.e y^2) and the last term (i.e 32) together. This gives 32y^2. Now we'll look for two factors of 32y^2 such that when we add them together it will result to the second term(i.e —12y) in the equation. These factors are —4y and —8y. Now we substitute these variables ( i.e —4y and —8y) in place of —12y in the equation above. This is illustrated below:
y^2 — 12y + 32 = 0
y^2 — 4y —8y + 32 = 0
Now we can factorize as follows
y(y —4) —8(y —4)
Since we same entities in the two brackets, we'll pick one:
(y —8)(y —4) = 0
y —8 = 0 or y — 4 = 0
y = 8 or y = 4
Therefore, the number is 4 or 8