If 3x^2 – 2x + 7 = 0, then (x – 1/3 )^2= ???? Having trouble with this one! Help!

Question

I believe this question uses the quadratic formula, but I can't seem to find the right answer. If someone could please explain this to me, I would greatly appreciate it. 

 

If 3x^{2 -} 2x + 7 = 0 Then (x-1/3)^{2 = ?}

Answer 1

If 3x² - 2x + 7 = 0 then x²-(2/3)x+7/3=0 

In solving by completion of the square we have

(x-1/3)²=x²-(2/3)x+1/9  The equation is

x²-(2/3)x++21/9=0 and so

(x-1/3)²+20/9=0 and so (x-1/3)²=-20/9.  No need to calculate the roots at all.

Answer 2

The quadratic formula will give two solutions that are complex numbers

(1+(2√5)i)/3= x1

X2 is the same but with a negative sign before 2√5i

(x-1/3)² = ((2√5)i)²/3 = -20/3

in the case using x2, will be =20/3

Answer 3

Hello Suzette,

 

You are correct, the quadratic formula will be needed to solve this problem! Remember the general form of the quadratic function to use the quadratic formula:

 

ax^2 + bx + c = 0

 

So if we compare this with the original problem, we find that a=3, b=-2, and c=7. 

 

Keep in mind that since this is a quadratic equation, that we will have two solutions for x! 

 

Good luck!