Question 70674
You are looking for an integer.  Call it x.
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The square of this integer is {{{x^2}}} and it is 56 more than the integer.  Therefore, if
you subtract {{{56}}} from the square of the integer the result should be the integer.
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The equation that expresses this is:
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{{{x^2 - 56 = x}}}
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Add minus x to both sides to eliminate the x term on the right side of the equation.
This changes the equation to:
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{{{x^2 - x -56 = 0}}}
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The left side of this equation factors:
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{{{(x-8)*(x+7) = 0}}}
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This equation will be true if either of the factors is zero, because 0 times anything on
the left side will make the left side equal zero.
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So one at a time set the factors equal to zero and solve for x.
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{{{x-8 = 0}}}
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By adding 8 to both sides the answer becomes {{{x=8}}}
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Next, set the other factor equal to zero:
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{{{x+7=0}}}
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By adding -7 to both sides the answer becomes {{{x = -7}}}
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Try these solutions to see if either or both works.  In the first case, square 8, subtract 56,
and see if the answer is 8.
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{{{8^2 - 56 = 64 - 56 = 8}}}
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That one works. For the next case square -7, subtract 56, and see if the answer is -7
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{{{(-7)^2 - 56 = 49 - 56 = -7}}}.
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That one works also.  So both answers ... {{{x = 8}}} and {{{x = -7}}} are good solutions.
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Hope this helps you to see your way through the problem.