Answer:
x = 1/3 + (2 i sqrt(5))/3 or x = 1/3 - (2 i sqrt(5))/3
Explanation:
Solve for x:
-3 x^2 + 2 x - 7 = 0
Divide both sides by -3:
x^2 - (2 x)/3 + 7/3 = 0
Subtract 7/3 from both sides:
x^2 - (2 x)/3 = -7/3
Add 1/9 to both sides:
x^2 - (2 x)/3 + 1/9 = -20/9
Write the left hand side as a square:
(x - 1/3)^2 = -20/9
Take the square root of both sides:
x - 1/3 = (2 i sqrt(5))/3 or x - 1/3 = -(2 i sqrt(5))/3
Add 1/3 to both sides:
x = 1/3 + (2 i sqrt(5))/3 or x - 1/3 = -(2 i sqrt(5))/3
Add 1/3 to both sides:
Answer: x = 1/3 + (2 i sqrt(5))/3 or x = 1/3 - (2 i sqrt(5))/3