Solve for x:
x (2 x + 3) = -8
Expand out terms of the left hand side:
2 x^2 + 3 x = -8
Divide both sides by 2:
x^2 + (3 x)/2 = -4
Add 9/16 to both sides:
x^2 + (3 x)/2 + 9/16 = -55/16
Write the left hand side as a square:
(x + 3/4)^2 = -55/16
Take the square root of both sides:
x + 3/4 = (i sqrt(55))/4 or x + 3/4 = -(i sqrt(55))/4
Subtract 3/4 from both sides:
x = (i sqrt(55))/4 - 3/4 or x + 3/4 = -(i sqrt(55))/4
Subtract 3/4 from both sides:
Answer: x = (i sqrt(55))/4 - 3/4 or x = -(i sqrt(55))/4 - 3/4
No real solutions