Solve the Equation by Using Substitution $$( 4 y + 7 ) ^ { 2 } = 4 ( 4 y + 7 ) + 6$$

question 116

Multiple Choice

Solve the equation by using substitution.
- $$( 4 y + 7 ) ^ { 2 } = 4 ( 4 y + 7 ) + 6$$

• A) \(\{ 2 + \sqrt { 10 } , 2 - \sqrt { 10 } \}\)
• B) \(\{ - 2 + \sqrt { 10 } , - 2 - \sqrt { 10 } \}\)
• C) \(\left\{ \frac { 5 } { 4 } + \frac { \sqrt { 10 } } { 4 } , \frac { 5 } { 4 } - \frac { \sqrt { 10 } } { 4 } \right\}\)
• D) \(\left\{ - \frac { 5 } { 4 } + \frac { \sqrt { 10 } } { 4 } , - \frac { 5 } { 4 } - \frac { \sqrt { 10 } } { 4 } \right\}\)

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Definitions:

Valid Argument

An argument whose structure ensures its conclusion follows logically from its premises, without contradiction.

Counterexample

An example that opposes or contradicts an argument or theory, often used to disprove general statements.

Valid Argument

A logical statement where, if the premises are true, the conclusion must necessarily follow, demonstrating sound reasoning and structure.

Reflexivity Relationship

A concept where actions in a system or process produce effects that feedback into the system, potentially influencing future actions.