Using the Quardic Formula Sove 3x^2+18x+24=0
To solve the quadratic equation 3x^2 + 18x + 24 = 0 using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients of the quadratic equation. In this case, the coefficient of x^2 is 3, the coefficient of x is 18, and the constant term is 24.
Step 2: Recall the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients in the quadratic equation.
Step 3: Substitute the values of a, b, and c from the quadratic equation into the quadratic formula. In this case, a = 3, b = 18, and c = 24.
x = (-18 ± √(18^2 - 4 * 3 * 24)) / (2 * 3)
Step 4: Simplify the expression within the square root.
x = (-18 ± √(324 - 288)) / 6
x = (-18 ± √36) / 6
x = (-18 ± 6) / 6
Step 5: Solve for x by simplifying further.
Option 1: x = (-18 + 6) / 6
x = -12/6
x = -2
Option 2: x = (-18 - 6) / 6
x = -24/6
x = -4
Therefore, the solutions to the quadratic equation 3x^2 + 18x + 24 = 0 are x = -2 and x = -4.