SOLUTION: i dont understand how you can turn this into a quadratic equation, The sum of the squares of three consecutive integers is 434. Find the integers. Help please. - Alex

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Question 1282: i dont understand how you can turn this into a quadratic equation,
The sum of the squares of three consecutive integers is 434. Find the integers.
Help please.
- Alex
Found 2 solutions by iamlegallyblond7, usyim88hk:
Answer by iamlegallyblond7(7) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of the squares of three consecutive integers.
well three consecutive integers are x, x+1, and x+2
so the squares of these integers are (x)^2, (x+1)^2, and (x+3)^2=
x^2, x^2+2x+1, and x^2+6x+9
so the sum of the squares are:
3x^2+8x+10=434
then you solve!

Answer by usyim88hk(157) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the smallest integer and x+1 be the second one and x+2 be the third one:
x^2 + (x+1)^2 + (x+2)^2 = 434
x^2 + (x^2+2x+1) + (x^2+4x+4) = 434
x^2+x^2+x^2+2x+4x+1+4 = 434
3x^2+6x-429 = 0 <---------- quadratic equation
Now use the quadratic formula to solve for x
x=%28-6%2B-sqrt%286%5E2-4%283%29%28-429%29%29%29%2F%282%283%29%29
x=%28-6%2B-sqrt%285184%29%29%2F6
x=%28-6%2B-72%29%2F6
x = 66/6 or -78/6
x = 11 or -13
So the three numbers can be [11, 12 ,13] or [-13, -12, -11]