SOLUTION: If x^2+6x+16=(x+a)^2+b for all values of x. Find a and b

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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

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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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