Answer:
x = -1/2 + (3 i)/2 or x = -1/2 - (3 i)/2
Explanation:
Solve for x:
4 x^2 + 4 x + 10 = 0
Divide both sides by 4:
x^2 + x + 5/2 = 0
Subtract 5/2 from both sides:
x^2 + x = -5/2
Add 1/4 to both sides:
x^2 + x + 1/4 = -9/4
Write the left hand side as a square:
(x + 1/2)^2 = -9/4
Take the square root of both sides:
x + 1/2 = (3 i)/2 or x + 1/2 = -(3 i)/2
Subtract 1/2 from both sides:
x = -1/2 + (3 i)/2 or x + 1/2 = -(3 i)/2
Subtract 1/2 from both sides:
Answer: x = -1/2 + (3 i)/2 or x = -1/2 - (3 i)/2