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a whole number increased by its square is two more than twice itself .find the the number

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MariHani99id
The answer is 2 because:
2 + (2^2) = 6    and     2 + (2 x 2) = 6
Let the whole number be x.

x + x²  = 2x + 2
x² + x - 2x - 2 = 0
x² - x - 2 = 0

Factor:
(x - 2) (x + 1) = 0

x - 2 = 0              x + 1 = 0
x = 2                  x = -1

The whole number is 2.

To check:
2 + 2² = 2 (2) + 2
2 + 4 = 4 + 2
6 = 6