SOLUTION: My question is 2 + √3x = x/3 Show far I have worked out. Multiply both sides by 3 3(2 + √3x) = x Then expanded bracket out 6 + 3√3x = x D

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: My question is 2 + √3x = x/3 Show far I have worked out. Multiply both sides by 3 3(2 + √3x) = x Then expanded bracket out 6 + 3√3x = x D      Log On


   

Question 331273: My question is
2 + √3x = x/3
Show far I have worked out.
Multiply both sides by 3
3(2 + √3x) = x
Then expanded bracket out
6 + 3√3x = x
Don't no if I have done correct so far and what to do next.
Any help would be gratefully recieved.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
My question is
2 + √3x = x/3
Show far I have worked out.
Multiply both sides by 3
3(2 + √3x) = x
Then expanded bracket out
6 + 3√3x = x
That's right so far, continuing
:
subtract 6 from both sides
3sqrt%283x%29 = x - 6
:
Square both sides
9(3x) = (x-6)^2
27x = x^2 - 12x + 36
:
A quadratic equation
x^2 - 12x - 27x + 36 = 0
x^2 - 39x + 36 = 0
:
This equation requires the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
In this problem; a=1; b=-39; c=36
x+=+%28-%28-39%29+%2B-+sqrt%28-39%5E2-4%2A1%2A36+%29%29%2F%282%2A1%29+
:
x+=+%2839+%2B-+sqrt%281521-144+%29%29%2F2+
:
x+=+%2839+%2B-+sqrt%281377+%29%29%2F2+
Two solutions
x+=+%2839+%2B+37.108%29%2F2+
x = 76.108%2F2
x = 38.054
and
x+=+%2839+-+37.108%29%2F2+
x = 1.892%2F2
x = .946
:
:
Check both solutions in original equation, only x=38.054 is a valid solution