The Following Is a Student S Solution for Solving $2 x ^ { 2 } = 1 - 5 x$

question 103

Essay

The following is a student s solution for solving $2 x ^ { 2 } = 1 - 5 x$ . What error did the student make?
$\begin{array} { l } 2 x ^ { 2 } = 1 - 5 x \\2 x ^ { 2 } - 1 + 5 x = 0 \\x = \frac { 1 \pm \sqrt { ( - 1 ) ^ { 2 } - 4 ( 2 ) ( 5 ) } } { 4 } \\x = \frac { 1 \pm \sqrt { 1 - 40 } } { 4 } \\x = \frac { 1 \pm \sqrt { - 39 } } { 4 } \\x = \frac { 1 } { 4 } \pm \frac { \sqrt { 39 } } { 4 } i\end{array}$

---

Definitions:

Slow-Wave Sleep

A stage of deep sleep characterized by low-frequency, high-amplitude EEG waves, essential for physical recovery and memory consolidation.

Activation-Synthesis Theory

A hypothesis that dreams are created by the higher brain centers interpreting random activity from the lower brain during REM sleep.

Limbic System

A complex system of nerves and networks in the brain, involving various areas near the edge of the cortex concerned with instinct and mood. It controls the basic emotions (fear, pleasure, anger) and drives (hunger, sex, dominance, care of offspring).

Burst Activity

Rapid firing of neurons in the brain, typically associated with specific behaviors or responses to stimuli.