SOLUTION: "suppose x^2+a^2x+a^2 factors into (x+a)^2. what is the value of a, that is not zero?"

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Question 183200: "suppose x^2+a^2x+a^2 factors into (x+a)^2. what is the value of a, that is not zero?"
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we're supposing that "x^2+a^2x+a^2 factors into (x+a)^2", this means that

x%5E2%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2


x%5E2%2Ba%5E2x%2Ba%5E2=%28x%2Ba%29%5E2 Start with the given equation.


x%5E2%2Ba%5E2x%2Ba%5E2=x%5E2%2B2ax%2Ba%5E2 FOIL the right side


cross%28x%5E2-x%5E2%29%2Ba%5E2x%2Ba%5E2=cross%28x%5E2-x%5E2%29%2B2ax%2Ba%5E2 Subtract x%5E2 from both sides. Note: the x%5E2 terms cancel out.


a%5E2x%2Bcross%28a%5E2-a%5E2%29=2ax%2Bcross%28a%5E2-a%5E2%29 Subtract a%5E2 from both sides. Note: the a%5E2 terms cancel out.


So we're left with:

a%5E2x=2ax


%28a%5E2%2Across%28x%29%29%2Fcross%28x%29=%282a%2Across%28x%29%29%2Fcross%28x%29 Divide both sides by "x". Once again, the "x" terms cancel


a%5E2=2a Simplify


a%5E2-2a=0 Subtract 2a from both sides.




a%28a-2%29=0 Factor the left side


Now set each factor equal to zero:

a=0 or a-2=0


a=0 or a=2 Now solve for "a" in each case


Note: since we want a value of "a" "that is not zero", this means that we'll ignore the value a=0

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Answer:

So the solution is a=2