Answer:
To solve the quadratic equation 3x^2 + 3x - 18 = 0 using the quadratic formula, we need to identify the coefficients a, b, and c in the general form of a quadratic equation, ax^2 + bx + c = 0.
In this case:
a = 3
b = 3
c = -18
Now we can substitute these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
x = (-(3) ± √((3)^2 - 4(3)(-18))) / (2(3))
Simplifying further:
x = (-3 ± √(9 + 216)) / 6
x = (-3 ± √225) / 6
Now, let's calculate the two possible solutions:
x1 = (-3 + √225) / 6
x2 = (-3 - √225) / 6
Calculating the square root of 225:
x1 = (-3 + 15) / 6 = 12 / 6 = 2
x2 = (-3 - 15) / 6 = -18 / 6 = -3
Therefore, the solutions to the quadratic equation 3x^2 + 3x - 18 = 0 are:
x1 = 2
x2 = -3