Solve the Equation $x \left( x - \frac { 2 } { 3 } \right) = 14$

question 48

Multiple Choice

Solve the equation $x \left( x - \frac { 2 } { 3 } \right) = 14$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)

• A) \(- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 1.54 ; - \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 2.21\)
• B) \(\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.42 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.09\)
• C) \(\frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 4.09 ; \frac { 1 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 3.42\)
• D) \(\frac { 2 } { 3 } + \frac { \sqrt { 127 } } { 6 } \approx 2.54 ; \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 6 } \approx - 1.21\)
• E) \(- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 3.42 ; - \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 4.42\)

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Speciation

The evolutionary process by which populations evolve to become distinct species, typically through genetic isolation from other populations.

Isolated Population

A group of organisms that is physically or genetically separated from others of the same species, leading to distinct evolutionary paths.

Sexual Isolation

It refers to a type of prezygotic barrier where different species are isolated from each other by differences in mating rituals, timing, or other behaviors, preventing mating.

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Proteins found in eggs, serving as a source of nutrition and playing roles in the development of the embryo.