Question

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

Answer 1

3x² - 2x + 7 = 0.

Using method of completing the square.

3x² - 2x = 0 - 7

3x² - 2x = -7          Divide through by 3.

x² - 2/3x = -7/3   ...........(d)

Coefficient of x = -2/3,  half of it = 1/2*-2/3 = -1/3    square of it = (-1/3)² = 1/9

We add (1/9) to both sides of equation (d)

x² - 2/3x = -7/3 

x² - 2/3x + 1/9 = -7/3 + 1/9

We factorize it by making using of half of the coefficient,  -1/3

(x - 1/3)² = -7/3 + 1/9

(x - 1/3)² = -20/9

That's the answer as asked by the question.   -20/9