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) \(- \frac { 1 } { 3 } + \frac { \sqrt { 127 } } { 3 } \approx 3.42 ; - \frac { 2 } { 3 } - \frac { \sqrt { 127 } } { 3 } \approx - 4.42\)

---

Definitions:

Molecular Terms

Language or terminology used to describe the composition, structure, and properties of molecules.

Natural Selection

Is the evolutionary process whereby organisms better adapted to their environment tend to survive and produce more offspring.

Instrumental Conditioning

A learning process in which behavior is modified by the consequences of actions, focusing on the use of rewards and punishments.

Positive Outcomes

Favorable results or benefits resulting from particular actions, behaviors, or interventions.