SOLUTION: the sum of an integer and its square is 6 less than the square of the next greater integer. what is the value of the integer?

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Question 17455: the sum of an integer and its square is 6 less than the square of the next greater integer. what is the value of the integer?
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the integer
then:
x + x%5E2 = %28x+%2B+1%29%5E2+-+6
so
x + x%5E2 = +%28x%5E2+%2B+2x+%2B+1%29+-+6 (if we multiply out %28x%2B1%29%5E2)
x + x%5E2 = x%5E2+%2B+2x+-+5
subtract x%5E2 from both sides
x = 2x - 5
add 5 to both sides
x + 5 = 2x
now subtract x from both sides
5 = x
check
5+%2B+5%5E2 = 30
%285%2B1%29%5E2+-+6 = 36 - 6 = 30
hope this helps