SOLUTION: What two numbers add and multiply to equal 144 and 18?

Question 572311: What two numbers add and multiply to equal 144 and 18?

Answer by mathsmiles(68) (Show Source): You can put this solution on YOUR website!
I'm going to guess you mean they multiply to 144 and they add to 18.

Let's choose X and Y for these two numbers.
X + Y = 18
X x Y = 144

Let's use substitution, which means we have to get either X or Y alone on one side of the equation:
X + Y = 18
X = 18 - Y

Now substitute this in place of X in the 2nd equation:
X x Y = 144
(18-y) x Y = 144 multiplying out the parens
18Y - Y^2 = 144 reordering:
-y^2 + 18Y = 144 subtracting 144 from both sides:
-y^2 + 18Y - 144 = 0

Just because I prefer to make life easier when possible, I'd like to get rid of the negative on the Y^2 term, so multiply both sides by -1.
-1(-y^2 + 18Y - 144) = -1(0)
y^2 - 18Y + 144 = 0
(Y - _)(Y - _) = 0
We need two factors of 144 whose sum is 18. Hmm...

Since two factors of 144 are 12 and 12, and other factors will be equally large, I don't see any way we're going to find two factors of 144 that add up to 18. This proves, I don't understand the problem the way you wrote it. Please correct it and re-submit.

All the details do matter. :-)

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