Question

Solve for x over the complex numbers.
x^2+10x+41=0
x=____ or x=____

Answer 1

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