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Question 851623: If a number is added with its square and when 28 is added , the resulting number is 300. What is that number?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! In order to solve, you need to convert this word problem into an equation. So, let's break this word problem down. Since we do not know the number, we can replace the unknown number with an x. We know that when this number (x), is added to it's square (x^2), and then 28 is added, we get 300. So,
x + x^2 + 28 = 300
This looks like a quadratic equation, doesn't it? Let's rewrite our equation in quadratic standard form of ax^2 + bx + c = 0:
x^2 + x - 272 = 0
Now, we can solve this equation through factoring, completing the square, or the quadratic formula. This can actually be factored, since 17 and -16 can be multiplied to give us -272, and added to give us 1. Hence,
(x - 16)(x + 17) = 0
Setting each term equal to zero will give us our two numbers:
x - 16 = 0 -----> x = 16
x + 17 = 0 -----> x = -17
So, our two numbers are 16 and -17.
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