SOLUTION: Number problem. The square of an interger is 56 more than the interger. Find the interger. I am lost on how to solve this problem and need some help with this problem please. Th

Question 70674This question is from textbook Beginning Algebra
: Number problem. The square of an interger is 56 more than the interger. Find the interger.
I am lost on how to solve this problem and need some help with this problem please. Thanks This question is from textbook Beginning Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You are looking for an integer. Call it x.
.
The square of this integer is and it is 56 more than the integer. Therefore, if
you subtract from the square of the integer the result should be the integer.
.
The equation that expresses this is:
.

.
Add minus x to both sides to eliminate the x term on the right side of the equation.
This changes the equation to:
.

.
The left side of this equation factors:
.

.
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.
.
So one at a time set the factors equal to zero and solve for x.
.

.
By adding 8 to both sides the answer becomes
.
Next, set the other factor equal to zero:
.

.
By adding -7 to both sides the answer becomes
.
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.
.

.
That one works. For the next case square -7, subtract 56, and see if the answer is -7
.
.
.
That one works also. So both answers ... and are good solutions.
.
Hope this helps you to see your way through the problem.
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