SOLUTION: Determine the constant that must be added to the given expression to complete the square and express the resulting trinomial as the square of a binomial 1. cē-4c 2. bē+4/3b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Determine the constant that must be added to the given expression to complete the square and express the resulting trinomial as the square of a binomial 1. cē-4c 2. bē+4/3b       Log On


   

Question 134394: Determine the constant that must be added to the given expression to complete the square and express the resulting trinomial as the square of a binomial
1. cē-4c
2. bē+4/3b
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Take half of the "c" coefficient to get -2. In other words, %281%2F2%29%2A%28-4%29=-2


Now square the result to get 4. In other words, %28-2%29%5E2=%28-2%29%28-2%29=4


So you must add 4 to the expression to get

c%5E2-4c%2B4

So the expression is now a perfect square




# 2

Take half of the "b" coefficient to get 4%2F6 or 2%2F3. In other words, %281%2F2%29%2A%284%2F3%29=4%2F6=2%2F3


Now square the result to get 4%2F9. In other words, %282%2F3%29%5E2=%282%2F3%29%282%2F3%29=4%2F9


So you must add 4%2F9 to the expression to get

b%5E2%2B%284%2F3%29b%2B4%2F9

So the expression is now a perfect square