the square of a certain whole number is 6 more than 5 times the whole number.

the square of X is 6 more than 5 times X.

             X² is 6 more than 5X.

             X² is 5X + 6

             X² = 5X + 6

    X² - 5X - 6 = 0

 (X - 6)(X + 1) = 0

X - 6 = 0;  X + 1 = 0
    X = 6;      X = -1

Negative numbers are not usually considered as whole numbers,
so I suppose we have to discard -1, though I'm not sure.

Answer: 6

The square of 6, which is 36 is 6 more than 5 times 6, which is 30.
Indeed 36 is 6 more than 30.

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If you wanted to consider -1 as also a solution, it DOES check.

The square of -1, which is +1 is 6 more than 5 times -1, which is -5.
Indeed +1 is 6 more than -5, because -5+6 = -1.

Edwin