Question 642151: x2-10x= ? find the number that should be added to each expression to make it a perfect square thanks for the help!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I can give you a recipe, but it is better to understand the rationale behind the procedure.
If you try to memorize a procedure, you may forget it, get confused, or remember it wrong.
I believe that if you understand why people do something a certain way, you will always remember just what you need to know to do it right every time. There's no need to memorize stuff in math.
THE RECIPE:
You need to look at the term in  .
(In this case, it is  ).
Divide it by 2. (You get  ).
Then divide that by the that is squared in the first term, the  term.
(You get  , which is an important part of the answer).
Next, square that number.
(You get  , which is the other important part of the answer).
Your answer is 
Your teacher prefer to see it as
THE RATIONALE
The square of a binomial (represented by  ) is given by
Your is  , your is  ,
and you are trying to find  and 
(Textbooks and teachers will also give you
 , but that is the same thing with  ).
Those formulas (and algebra in general) look like Greek to many people.
I like to see it as pictures and as real life issues.
I read that formula as
The square of a binomial (sum) is the sum of two squares plus two rectangles.
Imagine that you are adding to a square patio, to make a larger square patio.
It would look like this:
 As you add  to the length of your original blue by patio, you are adding the two green by rectangles on the sides,
and the red by square to fill the corner.
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