SOLUTION: (x-3)(x^2+3x-2) what formula do I use?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: (x-3)(x^2+3x-2) what formula do I use?      Log On


   

Question 471848: (x-3)(x^2+3x-2)
what formula do I use?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%28x%5E2%2B3x-2%29=0.
we know if x-3=0...->.....x=3........first solution

take x%5E2%2B3x-2=0 and complete the square

x%5E2%2B3x=2.....to the both sides add square of 1%2F2 of coefficient of middle term (which is 3): %28%281%2F2%293%29%5E2=%283%2F2%29%5E2

x%5E2%2B3x%283%2F2%29%5E2=2%2B%283%2F2%29%5E2
%28x%2B3%2F2%29%5E2=2%2B9%2F4
%28x%2B3%2F2%29%5E2=17%2F4
now we can apply square root method to find other two solutions
if u%5E2=d, then u=sqrt%28d%29 or u=-sqrt%28d%29
in your case u=%28x%2B3%2F2%29 and d=17%2F4
consequently
x%2B3%2F2=sqrt%2817%2F4%29
x%2B1.5=sqrt%284.25%29
x=2.06-1.5
x=0.56 ......second solution

or
x%2B3%2F2=-sqrt%2817%2F4%29
x%2B1.5=-sqrt%284.25%29
x=-2.06-1.5
x=-3.56 ........third solution
check:
%28x-3%29%28x%5E2%2B3x-2%29=0...x=3........first solution
%283-3%29%283%5E2%2B3%2A3-2%29=0
%280%29%289%2B9-2%29=0
0=0

%28x-3%29%28x%5E2%2B3x-2%29=0......x=0.56 ......second solution

%280.56-3%29%28%280.56%29%5E2%2B3%280.56%29-2%29=0

%28-2.44%29%280.3136%2B1.68-2%29=0
%28-2.44%29%281.9936-2%29=0
%28-2.44%29%282-2%29=0
%28-2.44%29%280%29=0
0=0
you can check third one by yourself