SOLUTION: if x^2+6x+16=(x+a)^2+b for all values of x, find the values of a and b

Question 156156: if x^2+6x+16=(x+a)^2+b for all values of x, find the values of a and b
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

FOIL

Subtract from both sides

Notice how the term is the only term on the right side that has an "x" in it. So this means that

Start with the given equation

Divide both sides by to isolate "a"

So the first answer is

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

Looking back at , the terms do not have an "x" term in them at all. So this means that

Start with the given equation

Plug in a=3

Square 3 to get 9

Subtract 9 from both sides

So the second answer is

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Answer:

So the solutions are and

Check:

works

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