Answer:
x = -3 + 2 i or x = -3 - 2 i
Step-by-step explanation:
Solve for x:
x^2 + 6 x + 13 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 13 from both sides:
x^2 + 6 x = -13
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 9 to both sides:
x^2 + 6 x + 9 = -4
Hint: | Factor the left hand side.
Write the left hand side as a square:
(x + 3)^2 = -4
Hint: | Eliminate the exponent on the left hand side.
Take the square root of both sides:
x + 3 = 2 i or x + 3 = -2 i
Hint: | Look at the first equation: Solve for x.
Subtract 3 from both sides:
x = -3 + 2 i or x + 3 = -2 i
Hint: | Look at the second equation: Solve for x.
Subtract 3 from both sides:
Answer: x = -3 + 2 i or x = -3 - 2 i
