The square of a number decreased by twice the number is equal to 28 more than the number. Find all possible values for the number

  -4 or 7

Step-by-step explanation:

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

  x^2 -2x = 28+x

  x^2 -3x = 28 . . . . . subtract x

  x^2 -3x +2.25 = 30.25 . . . . add the square of half the x coefficient

  (x -1.5)^2 = 30.25 . . . . . . . . write the left side as a square

  x -1.5 = ±5.5 . . . . . . . . . . . . take the square root

  x = 1.5 ±5.5 = {-4, 7} . . . . . . . add 1.5

The number may be either -4 or 7.

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