SOLUTION: Ok I need some help square 2x^2+5x+6=x If I subtract x I get 2x^2+4x+6=0 If I do that then it can't be factored right?

Question 133080: Ok I need some help square 2x^2+5x+6=x If I subtract x I get 2x^2+4x+6=0 If I do that then it can't be factored right?
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Does your equation look like this: ???

Start with the given equation

Square both sides

Subtract from both sides

Combine like terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our possible solutions are

or

However, we must check our answers:

Let's check the first possible solution

Start with the given equation

Plug in

Square and multiply

Combine like terms

Take the square root of 9 to get 3

Since the two sides are clearly not equal, this means that is an extraneous solution. In other words, is not a real solution.

---------------------

Let's check the first possible solution

Start with the given equation

Plug in

Square and multiply

Combine like terms

Take the square root of 4 to get 2

Since the two sides are clearly not equal, this means that is an extraneous solution. In other words, is not a real solution.

--------------------------------------
Answer:

So this shows us that does not have any solutions.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Well, that is not precisely correct. ALL quadratic trinomials can be factored, just not necessarily to integers, rationals, or even real numbers. In other words, for any second degree polynomial there exist two numbers and such that . It is just that in the case of your equation, , and are a conjugate pair of complex numbers, namely , where .

That means your factors would be

Having said all of that, I suspect you meant that the polynomial cannot be factored over the integers. That is an absolutely correct statement.
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