SOLUTION: Here is the problem: If 3x^2 - 2x + 7 = 0, then (x-1/3)^2 = I tried solving for x using the quadratic equation and arrived at 1 +or- 2sqrt(22) / 3. I'm not sure if this is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Here is the problem: If 3x^2 - 2x + 7 = 0, then (x-1/3)^2 = I tried solving for x using the quadratic equation and arrived at 1 +or- 2sqrt(22) / 3. I'm not sure if this is       Log On


   

Question 639486: Here is the problem:
If 3x^2 - 2x + 7 = 0, then (x-1/3)^2 =
I tried solving for x using the quadratic equation and arrived at 1 +or- 2sqrt(22) / 3. I'm not sure if this is correct, so could you walk me through it?
At that point, how could you plug that into (x-1/3)^2? There is more than one solution to x, so how could you arrive to one answer to that problem?
If it helps any, here are the possible choices: 20/9, 7/9, -7/9, -8/9, and -20/9
Thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the possible choices: 20%2F9=2.22, 7%2F9=0.77, -7%2F9=-0.77%7D%2C+%7B%7B%7B-8%2F9=-0.88, and -20%2F9=-2.22
If 3x%5E2+-+2x+%2B+7+=+0, then %28x-1%2F3%29%5E2 =?
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A7+%29%29%2F%282%2A3%29+
x+=+%282+%2B-+sqrt%28+4-84+%29%29%2F6+
x+=+%282+%2B-+sqrt%28+-80%29%29%2F6+
x+=+%282+%2B-+8.9i%29%2F6+
solutions:
x+=+%282+%2B8.9i%29%2F6+
x+=+2%2F6+%2B8.9i%2F6+
x+=+0.3333+%2B1.4833i+
or
x+=+%282+-8.9i%29%2F6+
x+=+2%2F6+-8.9i%2F6+
x+=+0.3333+-1.4833i+
then %28x-1%2F3%29%5E2 for x+=+0.3333+%2B1.4833i+ is
%280.3333+%2B1.4833i-1%2F3%29%5E2
=%280.3333+%2B1.4833i-0.33%29%5E2
=%28cross%280.3333%29+%2B1.4833i-cross%280.3333%29%29%5E2
=%281.4833i%29%5E2
=%281.4833%29%5E2%28i%29%5E2
=%282.2%29%28-1%29
=highlight%28-2.2%29
and, another solution:
%28x-1%2F3%29%5E2 for x+=+0.33+-1.48i+ is

%280.3333+-1.4833i-1%2F3%29%5E2
=%280.3333+-1.4833i-0.3333%29%5E2
=%28cross%280.3333%29+-1.4833i-cross%280.3333%29%29%5E2
=%28-1.4833i%29%5E2
=%28-1.4833%29%5E2%28i%29%5E2
=%28-2.2%29%28-1%29
=highlight%282.2%29