Solve the Equation by Completing the Square $$z ^ { 2 } + 10 z + 11 = 0$$

question 46

Multiple Choice

Solve the equation by completing the square.
- $$z ^ { 2 } + 10 z + 11 = 0$$

• A) \(5 \pm \sqrt { 11 }\)
• B) \(- 10 + \sqrt { 11 }\)
• C) \(- 5 \pm \sqrt { 14 }\)
• D) \(5 + \sqrt { 14 }\)

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Definitions:

Birch Reduction

A chemical reaction that reduces aromatic rings to cyclohexadienes using sodium or lithium in liquid ammonia, often with an alcohol as a proton source.

T-Butylbenzoic Acid

T-Butylbenzoic Acid is an organic compound with the structure derived from benzoic acid where a tert-butyl group is attached to the benzene ring.

Synthetic Steps

The sequenced actions taken in the laboratory to synthetically create or modify molecules.

Toluene

Toluene is a clear, water-insoluble liquid, widely used as an industrial feedstock and solvent, known for its role in the manufacture of benzene and as a component in gasoline.