Final answer:
The quadratic equation 6X^2 + 14X - 132 is solved using the general formula. The correct solutions are x = 11/3 and x = -6, with -6 being one of the provided options (Option C).
Step-by-step explanation:
To solve 6X^2 + 14X - 132 using the general formula for a quadratic equation ax² + bx + c = 0, we identify a = 6, b = 14, and c = -132. Then, we apply the quadratic formula:
x = −b ± √(b² - 4ac) / (2a)
Substituting the values, we have:
x = −14 ± √(14² - 4 × 6 × (−132)) / (2 × 6)
x = −14 ± √(196 + 3168) / 12
x = −14 ± √3364 / 12
x = −14 ± 58 / 12
Now, calculating the two possible solutions for x:
x = (−14 + 58) / 12 = 44 / 12 = 11/3
x = (−14 - 58) / 12 = −72 / 12 = −6
Therefore, the solutions are x = 11/3 (which is not one of the options given) and x = -6 (Option C).