Answer:
x = 1/7 + (2 i sqrt(5))/7 or x = 1/7 - (2 i sqrt(5))/7
Explanation:
Solve for x:
7 x^2 - 2 x + 3 = 0
Divide both sides by 7:
x^2 - (2 x)/7 + 3/7 = 0
Subtract 3/7 from both sides:
x^2 - (2 x)/7 = -3/7
Add 1/49 to both sides:
x^2 - (2 x)/7 + 1/49 = -20/49
Write the left hand side as a square:
(x - 1/7)^2 = -20/49
Take the square root of both sides:
x - 1/7 = (2 i sqrt(5))/7 or x - 1/7 = -(2 i sqrt(5))/7
Add 1/7 to both sides:
x = 1/7 + (2 i sqrt(5))/7 or x - 1/7 = -(2 i sqrt(5))/7
Add 1/7 to both sides:
Answer: x = 1/7 + (2 i sqrt(5))/7 or x = 1/7 - (2 i sqrt(5))/7