using the quadratic formula. find the solution to 3x^2 + 18x + 24 = 0
To find the solution to the quadratic equation 3x^2 + 18x + 24 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
For the given equation, we have:
a = 3, b = 18, and c = 24.
Substituting the values into the quadratic formula, we have:
x = (-(18) ± √((18)^2 - 4 * 3 * 24)) / (2 * 3)
Simplifying further:
x = (-18 ± √(324 - 288)) / 6
x = (-18 ± √36) / 6
Taking the square root:
x = (-18 ± 6) / 6
This gives us two possible solutions:
x1 = (-18 + 6) / 6 = -12 / 6 = -2
x2 = (-18 - 6) / 6 = -24 / 6 = -4
So, the solutions to the equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.