Answer:
x = (2 i)/sqrt(15) - 1 or x = -(2 i)/sqrt(15) - 1
Step-by-step explanation:
Solve for x:
18 x^2 + 33 x + 19 = 3 x (x + 1)
Expand out terms of the right hand side:
18 x^2 + 33 x + 19 = 3 x^2 + 3 x
Subtract 3 x^2 + 3 x from both sides:
15 x^2 + 30 x + 19 = 0
Divide both sides by 15:
x^2 + 2 x + 19/15 = 0
Subtract 19/15 from both sides:
x^2 + 2 x = -19/15
Add 1 to both sides:
x^2 + 2 x + 1 = -4/15
Write the left hand side as a square:
(x + 1)^2 = -4/15
Take the square root of both sides:
x + 1 = (2 i)/sqrt(15) or x + 1 = -(2 i)/sqrt(15)
Subtract 1 from both sides:
x = (2 i)/sqrt(15) - 1 or x + 1 = -(2 i)/sqrt(15)
Subtract 1 from both sides:
Answer: x = (2 i)/sqrt(15) - 1 or x = -(2 i)/sqrt(15) - 1
