SOLUTION: I need help completing the square of a quadratic equation. ] (3x^2)+(x)-(1/2)=0 The farthest I got before getting confused was this: (x+1/2)^2=5/12 Thank you for you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I need help completing the square of a quadratic equation. ] (3x^2)+(x)-(1/2)=0 The farthest I got before getting confused was this: (x+1/2)^2=5/12 Thank you for you      Log On


   

Question 432931: I need help completing the square of a quadratic equation. ]
(3x^2)+(x)-(1/2)=0
The farthest I got before getting confused was this:
(x+1/2)^2=5/12

Thank you for your time and help! =D
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I need help completing the square of a quadratic equation. ]
3x^2 + x - 1%2F2 = 0
We need the coefficient of x^2 to be 1, divide equation by 3, then we have
x^2 + 1%2F3x - 1%2F6 = 0
:
x^2 + 1%2F3x + ____ = 1%2F6
Find the value to complete the square; %281%2F2%2A1%2F3%29%5E2 = 1%2F36
x^2 + 1%2F3x + 1%2F36 = 1%2F6 + 1%2F36
x^2 + 1%2F3x + 1%2F36 = 6%2F36 + 1%2F36
x^2 + 1%2F3x + 1%2F36 = 7%2F36
Which is
%28x+%2B+1%2F6%29%5E2 = 7%2F36
Find the square root of both sides
x + 1%2F6 = +/-sqrt%287%2F36%29
extract the perfect square
x + 1%2F6 = +/-%281%2F6%29sqrt%287%29
Two solutions
x = -1%2F6 + %281%2F6%29sqrt%287%29
and
x = -1%2F6 - %281%2F6%29sqrt%287%29
we can write it
x = %28-1%2Bsqrt%287%29%29%2F6
and
x = %28-1-sqrt%287%29%29%2F6