Answer: To use the method of completing the square to solve the quadratic equation x^2 + x + 9 = 0, we can follow these steps:
Move the constant term to the right-hand side of the equation:
x^2 + x = -9
Add the square of half the coefficient of the x-term to both sides of the equation:
x^2 + x + (1/2)^2 = -9 + (1/2)^2
x^2 + x + 1/4 = -35/4
Rewrite the left-hand side as a square:
(x + 1/2)^2 = -35/4 + 1/4
(x + 1/2)^2 = -34/4
Take the square root of both sides:
x + 1/2 = ±sqrt(-34/4)
Solve for x:
x = -1/2 ± sqrt(-34)/2
So the number that needs to be added to "complete the square" is (1/2)^2 = 1/4.
Explanation: