SOLUTION: The square of a negative integer minus itself is 110. Find the integer.

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Question 253100: The square of a negative integer minus itself is 110. Find the integer.
Found 2 solutions by hokies, jim_thompson5910:
Answer by hokies(65) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - x = 110.
x^2 - x - 110 = 0.
To factor this, what two numbers multiply to -110 but add up to -1? The answer is -11 and 10, so:
(x-11)*(x+10)=0
Solving this equation, we get: x = 11 and x = -10. Choose the negative solution: x=-10.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since "The square of a negative integer minus itself is 110", this means that x%5E2-x=110


x%5E2-x=110 Start with the given equation.


x%5E2-x-110=0 Subtract 110 from both sides.


Notice that the quadratic x%5E2-x-110 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-1, and C=-110


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-110%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-110


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-110%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%28-110%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--440+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-110%29 to get -440


x+=+%281+%2B-+sqrt%28+1%2B440+%29%29%2F%282%281%29%29 Rewrite sqrt%281--440%29 as sqrt%281%2B440%29


x+=+%281+%2B-+sqrt%28+441+%29%29%2F%282%281%29%29 Add 1 to 440 to get 441


x+=+%281+%2B-+sqrt%28+441+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+21%29%2F%282%29 Take the square root of 441 to get 21.


x+=+%281+%2B+21%29%2F%282%29 or x+=+%281+-+21%29%2F%282%29 Break up the expression.


x+=+%2822%29%2F%282%29 or x+=++%28-20%29%2F%282%29 Combine like terms.


x+=+11 or x+=+-10 Simplify.


So the possible solutions are x+=+11 or x+=+-10


But since we're told that the integer is negative, this means that the only solution is x=-10