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

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) (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) (Show Source): You can put this solution on YOUR website!
Since "The square of a negative integer minus itself is 110", this means that

Start with the given equation.

Subtract 110 from both sides.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

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