Solve the Equation by Completing the Square $$2 x ^ { 2 } + 12 x + 3 = 0$$

question 178

Multiple Choice

Solve the equation by completing the square.
- $$2 x ^ { 2 } + 12 x + 3 = 0$$

• A) \(\left\{ \frac { - 12 - \sqrt { 30 } } { 2 } , \frac { - 12 + \sqrt { 30 } } { 2 } \right\}\)
• B) \(\left\{ \frac { - 6 - \sqrt { 30 } } { 2 } , \frac { - 6 + \sqrt { 30 } } { 2 } \right\}\)
• C) \(\left\{ \frac { - 6 - \sqrt { 30 } } { 4 } , \frac { - 6 + \sqrt { 30 } } { 4 } \right\}\)
• D) \(\left\{ \frac { - 6 - \sqrt { 42 } } { 2 } , \frac { - 6 + \sqrt { 42 } } { 2 } \right\}\)

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Definitions:

Same Direction

Refers to variables that move or change in unison, indicating a positive correlation where if one increases, the other also increases, and vice versa.

Chocolate Chip Cookie Dough

A mixture used to bake chocolate chip cookies, often considered for its raw consumption appeal as well.

Elastic

Describes a situation in which the supply or demand for a good or service is highly responsive to changes in price.

Good Substitutes

Products or services that can be used in place of one another, where the increase in price of one leads to an increase in demand for the other.