SOLUTION: Please help me solve for x in the equation {{{x^2-(a+3b)x+3ab=0}}}.

Algebra ->  Functions -> SOLUTION: Please help me solve for x in the equation {{{x^2-(a+3b)x+3ab=0}}}.      Log On


   

Question 979447: Please help me solve for x in the equation x%5E2-%28a%2B3b%29x%2B3ab=0.
Found 2 solutions by josgarithmetic, Edwin McCravy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Using formula for general solution of quadratic equation,
x=%28a%2B3b%2B-+sqrt%28%28a%2B3b%29%5E2-4%2A3ab%29%29%2F2

Look for a possible simplification
%28a%2B3b%2B-+sqrt%28a%5E2%2B6ab%2B9b%5E2-12ab%29%29%2F2

%28a%2B3b%2B-+sqrt%28a%5E2-6ab%2B9b%5E2%29%29%2F2

%28a%2B3b%2B-+sqrt%28%28a-3b%29%5E2%29%29%2F2

%28a%2B3b%2B-+%28a-3b%29%29%2F2

%28a%2B3b-a%2B3b%29%2F2
6b%2F2
highlight%283b%29
OR
%28a%2B3b%2Ba-3b%29%2F2
2a%2F2
highlight%28a%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-%28a%2B3b%29x%2B3ab=0

Distribute to remove the parentheses:

x%5E2-ax-3bx%2B3ab=0

Factor x out of the first two terms

x%28x-a%29-3bx%2B3ab=0

Factor -3b out of the last two tems:

x%28x-a%29-3b%28x-a%29=0

Factor (x-a) out of both terms:

%28x-a%29%28x-3b%29=0

Use the zero-factor property:

x-a=0     x-3b=0
  x=a       x=3b

Edwin