Question 783793: What do you think it means when A is not 1 when we attempt to complete the square? For example, 5x squared + 25x + 10 = 45 what A represents or B tell me how to make A = 1
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! What is the meaning of A and B?
You give an equation and you give a mention about A and B but nowhere indicate what these two variables mean.
A best-guess is that the A and B are part of the more general,  quadratic equation. You do NOT make A=1. In your given equation,  , A=5. Also, B=25. You can Complete the Square if you like, but A=5 and B=25 whatever you do.
What you want when you Complete the Square is to factorize the quadratic expression in your equation which effectively gives you a quadratic expression in which the coefficient on  will be 1. Your left side would go like this:
and you would determine that the square term to add & subtract, or to just add to both sides of the equation, would be  , which corresponds to the more general  .
Note, what I should also say,
WITHIN the quadratic factor,  , A=1 and B=5, but this is only if we first ignore labeling the coefficients in the original equation and focus only on the coefficients in the quadratic factor. To say that A=1 and A=5 is really a BAD IDEA.
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