SOLUTION: The sum of a positive number and its square is 12. What is the number?

Question 185547: The sum of a positive number and its square is 12. What is the number?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"The sum of a positive number and its square is 12" translates to

Start with the given equation.

Subtract 12 from both sides.

Rearrange the terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, the problem states that the number is positive. So we must ignore

So the only answer is which means that the number is 3

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