SOLUTION: if 3x^2-2x+7=0, then (x-1/3)^2= A. 20/9 B. 7/9 C. -7/9 D. -8/9 E. -20/9 (im studying for college)

Algebra ->  Equations -> SOLUTION: if 3x^2-2x+7=0, then (x-1/3)^2= A. 20/9 B. 7/9 C. -7/9 D. -8/9 E. -20/9 (im studying for college)      Log On


   

Question 1119035: if 3x^2-2x+7=0, then (x-1/3)^2=
A. 20/9
B. 7/9
C. -7/9
D. -8/9
E. -20/9
(im studying for college)
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The term to complete the square for the quadratic equation is %281%2F3%29%5E2.

3%28x%5E2-2x%2F3%2B%281%2F3%29%5E2%29=-7%2B3%281%2F3%29%5E2
3%28x-1%2F3%29%5E2=-7%2B1%2F3
%28x-1%2F3%29%5E2=%281%2F3-7%29%2F3-------continue to simplify the right side and you should have what was asked.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

if 3x^2-2x+7=0, then (x-1/3)^2=
A. 20/9
B. 7/9
C. -7/9
D. -8/9
E. -20/9
(im studying for college)
matrix%281%2C3%2C+3x%5E2+-+2x+%2B+7%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+3x%5E2+-+2x%2C+%22=%22%2C+-+7%29 -------- Subtracting 7 from both sides

matrix%281%2C3%2C+3x%5E2%2F3+-+%282%2F3%29x%2C+%22=%22%2C+-+7%2F3%29 ----- Dividing by 3 to make the leading coefficient, 1 

matrix%281%2C3%2C+x%5E2+-+%282%2F3%29x%2C+%22=%22%2C+-+7%2F3%29

  ------ Completing the square on x



matrix%281%2C3%2C+%28x+-+1%2F3%29%5E2%2C+%22=%22%2C+-+7%2F3+%2B+1%2F9%29

matrix%281%2C3%2C+%28x+-+1%2F3%29%5E2%2C+%22=%22%2C+-+21%2F9+%2B+1%2F9%29

 (CHOICE E)

Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
I only want to add that THERE IS NO real number x, satisfying the given equation and satisfying this equality 


%28x-1%2F3%29%5E2 = -20%2F9.    (*)


It can be true for complex numbers ONLY.


How did I reveal it ?  - Look in this equality (*): the square of a number in the left side is equal to negative number in the right side.


There is nothing bad in it; you only need to understand it that there is no such real number.

----------------
Also,  on completing the square see the lesson
    - HOW TO complete the square - Learning by examples
in this site.