SOLUTION: Find numbers a and b so that x^2+4x+9=(x+a)^2+b

Question 123071: Find numbers a and b so that x^2+4x+9=(x+a)^2+b
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Subtract from both sides

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of does not change the equation

Now factor to get

Now add to both sides to isolate y

Combine like terms

So what we've done is complete the square and convert into

So this means that which in turn also means

Here we can see that and

Answer:

So our answers are: and
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