SOLUTION: The square of a certain number is 22 less than 13 times the original. Find the answer?

Question 707084: The square of a certain number is 22 less than 13 times the original. Find the answer?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Using "x" to represent the original number, "The square of a certain number is 22 less than 13 times the original" translates into:

(Note how in English the "22 less" was first but when we translate it into a mathematical expression it goes at the end. This is usually how it works. If this seems confusing just think of this: If someone asked to figure out 22 less than 45, what would you do? 22-45 or 45-22?

To solve our equation we first want one side to be zero. Subtracting 13x from each side and adding 22 to each side we get:

Now we factor (or use the Quadratic Formula). This factors fairly easily:

Now we use the Zero Product Property which tells us that a product that equals zero, like ours, can only happen if one of the factors is zero. So:
x-2 = 0 or x-11 = 0
Solving these we get:
x = 2 or x = 11

So there are two possible answers to the problem. You can check if you like:

Both of these check out.
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