Question 747677: I would like some help on a problem concerning quadratic equations. Here is the problem. There are three consecutive numbers. When the largest one is squared, it is equal to 18 more than 9 times the smallest number. x^2+4x+4=9x+18. Please explain thoroughly and clearly, as I am in a deep fix. Can you also give me the three consecutive numbers? Thank you in advance
Found 3 solutions by stanbon, MathTherapy, mikeebsc:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! There are three consecutive numbers. When the largest one is squared, it is equal to 18 more than 9 times the smallest number.
Please explain thoroughly and clearly, as I am in a deep fix. Can you also give me the three consecutive numbers?
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1st: x-1
2nd: x
3rd: x+1
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Equation:
(x+1)^2 = 9(x-1)+18
x^2 + 2x + 1 = 9x-9+18
x^2 -7x -8 = 0
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(x-8)(x+1) = 0
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Positive solution:
x = 8
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1st: x-1 = 7
2nd: x = 8
3rd: x+1 = 9
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Cheers,
Stan H.
Answer by MathTherapy(10552)  (Show Source):
Answer by mikeebsc(26) (Show Source):
You can put this solution on YOUR website! I am so sorry I do not know how to make the equations on this site, I just started. In doing the math however, the three consecutive numbers are 7, 8, 9.
9^2=81 (the largest squared)
9*7=63 (9 times the smaller number)
63+18=81 (equal to 18 more than 9 times 7(the smaller number))
I am truly sorry I do not have the ability to show you the quadratic equation part. I'm sure someone will take this up, but at least you have your 3 numbers and maybe that can even get you going with the quadratic equation.
**edit**
I see that Stan took care of you with the math part. Awesome:). He is definitely a math genius.
**2nd edit**
I also see therapy took care of it...I've been posting on this site for 2 days and they both stick out to me already as 2 of the smartest here. I was trying to do what "therapy" did with posting the regular equations and just haven't been around long enough to know how. It's nice to see my math confirmed though, as that is is the way I did it. Stan's way is pretty cool too. Keep posting any problems you have, if you need any personal help, you can reach me through the thank you thing. I'm sure the other 2 would oblige as well.
**a little more**
I see you asked for thorough explanation. So, what happened was, we subtracted 9x and 18 from both sides to get all terms to one side and set the equation to 0.
Then we factored to get (x-7)(x+2)
Then we solved for x by setting each factor equal to 0: x-7=0, then added 7 to both sides to get x=7. With x+2=0 we subtracted 2 from both sides to get x=-2.
Good Luck,
Mike
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