SOLUTION: Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. X^2+5/6x

Algebra ->  Equations -> SOLUTION: Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. X^2+5/6x      Log On


   

Question 983024: Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. X^2+5/6x
Found 2 solutions by macston, MathLover1:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2%2B%285%2F6%29x=0
Take 1/2 of the co-efficient of x:
%281%2F2%29%285%2F6%29=5%2F12 (Remember this)
Square it:
%285%2F12%29%5E2=25%2F144
Add to both sides of the original equation:
x%5E2%2B%285%2F6%29x%2B%2825%2F144%29=%2825%2F144%29
Using the number you remembered above, write the left side as a square:
%28x%2B5%2F12%29%5E2=25%2F144 The sign is the parenthesis is the same as the sign of the co-efficient of x in the original equation (+(5/6)x so the sign is +)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the discriminant must be equal to 0 for perfect square polynomials
so, add a variable for the constant k, then get a formula for the discriminant %28b%5E2+-+4ac%29, then determine the value of k to make it 0
x%5E2%2B%285%2F6%29x%2Bk
%28b%5E2+-+4ac%29=+0
%28%285%2F6%29%5E2+-+4%2A1%2Ak%29=0
25%2F36-+4k=0
25%2F36=4k
%2825%2F36%29%2F4=k
k=25%2F144+
x%5E2%2B%285%2F6%29x%2B25%2F144
%28x%5E2%2B25%2F144%29%5E2

or simple, take half of the x-coefficient %285%2F6%29 to get %285%2F12%29, then
square %285%2F12%29 to get %2825%2F144%29 and that is your constant k
you need to add
x%5E2%2B%285%2F6%29x%2Bk
x%5E2%2B%285%2F6%29x%2B25%2F144
%28x%5E2%2B25%2F144%29%5E2