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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B16x%2Ba=%28x%2Bb%29%5E2 Start with the given equation.


x%5E2%2B16x%2Ba=x%5E2%2B2xb%2Bb%5E2 FOIL the right side.

Take note that the terms 16x and 2xb both have "x" terms (without an exponent). So this means that 16x=2xb. Divide both sides by 2x to get 8=b or b=8

Notice how the term "a" does not have an "x" and b%5E2 doesn't have an "x" either. So this means that a=b%5E2.


Plug in b=8 to get a=8%5E2=64. So a=64


So this tells us that x%5E2%2B16x%2B64=%28x%2B8%29%5E2