What value should be added to the expression to create a perfect square

label Algebra
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x^2-20x

Mar 10th, 2015

-first you have to consider the formula a perfect square: (aX+b)^2=(aX)^2+(2)(a)(b)+b^2

-You have to match the equation on the right with the problem. 

-in the problem the number in from of x^2 is one  and the number in form of X^2 in the formula is a. So a=1

-next look at the number in front of X in the problem: -20: and the number in front of X in the the formula is 2ab

so 2ab=-20 (a=1) so 2b=-20 and b=-10

-They problem has given you two of the three terms in the formula, but is missing is b^2. From above you know that b=-10 thus b^2=(-10)^2=100. what need to be added to the expression is 100.

-(x-10)^2=x^2-20x+100

Hope that helps. :)

Mar 10th, 2015

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Mar 10th, 2015
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