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(q+a)2 = q2 + 2aq + a2
You have 3q and you need to find a value for a so that
3q = 2aq
3 = 2a
3/2 = a
So,
(q + 3/2)2 = q2 + 3q + 9/4
_____
This is called "completing the square". It is the basis of a recognized method of solving a quadratic equation, and is the basis of the quadratic formula.
You have 3q and you need to find a value for a so that
3q = 2aq
3 = 2a
3/2 = a
So,
(q + 3/2)2 = q2 + 3q + 9/4
_____
This is called "completing the square". It is the basis of a recognized method of solving a quadratic equation, and is the basis of the quadratic formula.
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