Solve for x: x^2 + 10 x + 41 = 0 Subtract 41 from both sides: x^2 + 10 x = -41 Add 25 to both sides: x^2 + 10 x + 25 = -16 Write the left hand side as a square: (x + 5)^2 = -16 Take the square root of both sides: x + 5 = 4 i or x + 5 = -4 i Subtract 5 from both sides: x = -5 + 4 i or x + 5 = -4 i Subtract 5 from both sides: Answer: x = -5 + 4 i or x = -5 - 4 i
