SOLUTION: If 3x^2-2x+7=0, then (x-1/3)^2=??

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If 3x^2-2x+7=0, then (x-1/3)^2=??      Log On


   

Question 465377: If 3x^2-2x+7=0, then (x-1/3)^2=??
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If 3x^2-2x+7=0
Solve for "x":
x = [2+-sqrt(4-4*3*7)]/6
---
x = [2 +- sqrt(80)]/6
---
x = [2 +- 4sqrt(3)]/6
----
x = [1 + 2sqrt(3)]/3 or x = [1 - 2sqrt(3)]/3
=================================================
then (x-1/3)^2=??
---
If x = [1+2sqrt(3)]/3
then (x-(1/3)^2
= [[1+2sqrt(3)]/3 - (1/3)]^2
= [2sqrt(3)/3]^2
= 4/3
----
If x = [1-2sqrt(3)]/3
then (x-(1/3)^2 = 4/3
==========================
Cheers,
Stan H.