Answer :
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
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