SOLUTION: What must be added to x2^-7x to make it a perfect square?

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Question 1009335: What must be added to x2^-7x to make it a perfect square?
Found 2 solutions by fractalier, MathLover1:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
You take half the x-term coefficient and square it...thus from
x^2 - 7x, we take half of -7 and get -3.5, then square it and get
12.25
so that x^2 - 7x + 12.25 = (x - 3.5)^2
a perfect square...

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+x%5E2-7x.......recall:%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2; so, to make it perfect square we need to add b%5E2
+x%5E2-7x%2Bb%5E2...when you compare it to a%5E2-2ab%2Bb%5E2, you see that a=1 and 2ab=7
now we can find b:
2ab=7=>2%2A1%2Ab=7=>b=7%2F2
then we have:
+x%5E2-7x%2B%287%2F2%29%5E2
+%28x-7%2F2%29%5E2