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Solve 6X^2 + 14X - 132 using the general formula.

A. X = -4
B. X = 2
C. X = -6
D. X = 6

1 Answer

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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).

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