SOLUTION: a whole number increased by its square is twenty more than twice itself. a.) write and equation that represents the statement b.)solve the equation and find the number

Question 971192: a whole number increased by its square is twenty more than twice itself.
a.) write and equation that represents the statement
b.)solve the equation and find the number
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
w, the whole number

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There is a problem with the way you have posed this question from the beginning. While most authorities that I have ever consulted say that the term whole number refer to the set of non-negative integers, some few insist that the term refers to all integers. Why is this a problem? Because using the more restrictive definition, your problem has exactly one element in the solution set whereas under the broader definition, there are two correct answers.

Writing the problem exactly as it reads:

Putting the quadratic into standard form:

Factor:

is certainly a solution, but you need to figure out what your instructor, professor, teacher, textbook, or other authority means when they say "whole number" before you decide whether to include

By the way, you can utterly avoid the problem for the rest of your life if you forget you ever heard the terms "whole numbers", "counting numbers", or "natural numbers". Rather, use:

Integers
Negative Integers (does not include zero)
Non-Positive Integers (includes zero)
Non-Negative Integers (includes zero)
Positive Integers (does not include zero)

These terms are defined the same way universally eliminating any possibility of confusion.

John

My calculator said it, I believe it, that settles it

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