SOLUTION: x^2+16x+a=(x+b)^2 ^^In the equation above, a and b are constants. If the equation is true for all values of x, what is the value of a?

Question 175846: x^2+16x+a=(x+b)^2
^^In the equation above, a and b are constants. If the equation is true for all values of x, what is the value of a?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

FOIL the right side.

Take note that the terms 16x and 2xb both have "x" terms (without an exponent). So this means that . Divide both sides by 2x to get or

Notice how the term "a" does not have an "x" and doesn't have an "x" either. So this means that .

Plug in to get . So

So this tells us that
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