Question

If number is added to its square, the result is 56. find the number.

Answer 1

-8 or +7

Explanation:

Let x represent the number. The the problem statement tells us ...

x² + x = 56

x² +x -56 = 0 . . . . . subtract 56 to put into standard form

(x +8)(x -7) = 0 . . . . factor

Solutions to the equation are values of x that make the factors zero:

x = -8 . . . or . . . x = +7

The number could be -8 or +7.

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Check

For x = -8, the square is (-8)² = 64. Adding -8 to that gives 64-8 = 56.

For x = 7, the square is 7² = 49. Adding 7 to that gives 49+7 = 56.