Answer: The solutions to the equation x^2 + 11x + 18 = 0 are x = -2 and x = -9.
Step-by-step explanation: To solve this equation, we need to factorize the quadratic expression or use the quadratic formula.
Method 1: Factorization
We need to find two numbers whose product is 18 and sum is 11. These numbers are 9 and 2. Therefore,
x^2 + 11x + 18 = 0
(x + 9)(x + 2) = 0
So the solutions are:
x + 9 = 0 or x + 2 = 0
x = -9 or x = -2
Method 2: Quadratic formula
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Substituting the values from the given equation into the formula, we get:
x = (-11 ± sqrt(11^2 - 4(1)(18))) / 2(1)
x = (-11 ± sqrt(121 - 72)) / 2
x = (-11 ± sqrt(49)) / 2
So the solutions are:
x = (-11 + 7) / 2 or x = (-11 - 7) / 2
x = -2 or x = -9