Solve the Equation by Completing the Square $$x ^ { 2 } + 8 x = 7$$

question 421

Multiple Choice

Solve the equation by completing the square.
- $$x ^ { 2 } + 8 x = 7$$

• A) \(\{ - 4 \pm \sqrt { 23 } \}\)
• B) \(\{ - 1 \pm \sqrt { 23 } \}\)
• C) \(\{ - 4 \pm 1 \sqrt { 23 } \}\)
• D) \(\{ 4 + \sqrt { 23 } \}\)

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Definitions:

Profit-maximizing Output

The level of production at which a firm achieves the highest possible profit, determined where marginal cost equals marginal revenue.

Marginal Product

The additional output that is produced by adding one more unit of a specific input, holding all other inputs constant.

Purely Competitive Market

A market structure characterized by many buyers and sellers, free entry and exit, and a homogeneous product, leading to price taking behavior.

Economic Profit

The difference between the total revenue generated by a business and its total costs, including both explicit and implicit costs.