1 added to a positive number gives the square of the number find the number
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Answer:
For these types of problem you need to learn how to translate the words into a formula.
In your statement, the words “the result is” means “equals”.
The words “you square 5 more than a positive number” means (n+5)^2, where n stands in for some positive number.
The words “88 more than 12 times the number” means 12n+88.
If you understand what I wrote above, you will be able to translate the question into the following equation.
(n+5)^2 = 12n + 88
Now you just have to solve this equation for n.
(n+5)^2 = (n+5) * (n+5) =
n^2 +10n + 25 = 12n + 88
Subtracting (12n +88) from both sides yields
n^2 - 2n -63 = 0
You are going to end up with a quadratic equation which you will need to factor to get two possible answers.
Think of two numbers which multiplied together give you -63 and added together give you -2. The two that pop into my head are 7 and -9. Try these to write the quadratic equation as a multiple of two simpler equations.
How about (n+7)*(n-9)
This equals n (n-9) + 7(n-9) or n^2 -9n +7n -63 or
n^2 -2n -63
So we know that (n+7) * (n-9) = 0
Here is the part that my teacher skipped over when I was in grade 10. If some number a times some other number b is equal to zero, then both a and b are equal to zero.
a*b=0
If you divide both sides by a, you get b=0/a which equals 0. If you divide both sides by b, you get a=0/b which is also 0.
So, n+7=0 and n-9=0
So your two answers are n=-7 and n=9. But, your question states that n is a positive number. So n=9 is the only answer that works.
Let’s plug 9 into the equation in place of n and check it out.
(9+5)^2 = 12*9 + 88
14^2 = 108+88
196=196
Answer:
i Don't know this question
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