Answer : x = 3 and -2
Explanation:
To solve the quadratic equation 3x² - 3x - 18 = 0, we can start by factoring the equation. Once we have the factors, we can set each factor equal to zero and solve for x. Let's proceed with the factoring:
3x² - 3x - 18 = 0
First, we can factor out the greatest common factor, which is 3:
3(x² - x - 6) = 0
Now, we need to factor the quadratic expression inside the parentheses:
The quadratic expression can be factored into two binomials:
(x - a)(x - b)
We need to find two numbers, "a" and "b," such that their product is the coefficient of the quadratic term (1) times the constant term (-6), and their sum is the coefficient of the linear term (-1).
The pair of numbers that fits these conditions is -3 and 2, because:
-3 * 2 = -6
-3 + 2 = -1
So, the factored form becomes:
3(x - 3)(x + 2) = 0
Now we can set each factor equal to zero and solve for x:
x - 3 = 0 -> x = 3
x + 2 = 0 -> x = -2
So, the solutions for the equation 3x² - 3x - 18 = 0 are x = 3 and x = -2.