Question

F(x) = -3x2 + 2x - 7

Answer 1

Answer:

x = 1/3 + (2 i sqrt(5))/3 or x = 1/3 - (2 i sqrt(5))/3

Step-by-step 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