SOLUTION: Please help with this! I need to solve by completing the square: 3x^2 -2x = 0 and x^2 + 100 = 27x Thanks so much!!

Algebra ->  Rational-functions -> SOLUTION: Please help with this! I need to solve by completing the square: 3x^2 -2x = 0 and x^2 + 100 = 27x Thanks so much!!      Log On


   

Question 532001: Please help with this! I need to solve by completing the square:
3x^2 -2x = 0
and x^2 + 100 = 27x

Thanks so much!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 - 2x + __ = 0
to complete the square we need the coefficient of x^2 to 1, divide eq by 3,
x^2 - 2%2F3x + ____ = 0
to obtain the term that completes the square, divide the coefficient of x by 2 and square it.
Add of both sides
x^2 - 2%2F3x + 1%2F9 = 1%2F9
A perfect squares which factors to
%28x+-+1%2F3%29%5E2 = 1%2F9
find the square root of both sides
%28x+-+1%2F3%29 = +/-sqrt%281%2F9%29
Find the square root of 1/9
x = 1%2F3 +/-1%2F3
Two solutions
x = 1%2F3 + 1%2F3
x = 2%2F3
and
x = 1%2F3 - 1%2F3
x = 0
:
:
x^2 + 100 = 27x
Write it in this form
x^2 - 27x + ___ = -100
Find the 3rd term that completes the square, (27/2)^2
x^2 - 27x + 729%2F4 = -100 + 729%2F4
x^2 - 27x + 729%2F4 = -400%2F4 + 729%2F4
x^2 - 27x + 729%2F4 = 329%2F4
%28x+-+27%2F2%29%5E2 = 329%2F4
Find the square root of both sides
%28x+-+27%2F2%29 = +/- sqrt%28329%2F4%29
x = 27%2F2%29 +/- sqrt%28329%2F4%29
Extract the square root of 1/4
x = 27%2F2%29 +/- 1%2F2*sqrt%28329%29
Two solutions
x = %2827+%2B+sqrt%28329%29%29%2F2
and
x = %2827+-+sqrt%28329%29%29%2F2