Solving Quadratic Equations: Completing the Square — Quiz

Question 6 • Algebra: Concepts and Connections

Which are the solutions of the quadratic equation? x squared is equal to 9 x plus 6

Answer

the fraction with numerator negative 9 minus square root of 105 and denominator 2 comma the fraction with numerator negative 9 plus square root of 105 and denominator 2

the fraction with numerator 9 minus square root of 105 and denominator 2 comma the fraction with numerator 9 plus square root of 105 and denominator 2

the fraction with numerator 9 minus square root of 57 and denominator 2 comma the fraction with numerator 9 plus square root of 57 and denominator 2

the fraction with numerator negative 9 minus square root of 57 and denominator 2 comma the fraction with numerator negative 9 plus square root of 57 and denominator 2

Explanation

Rewrite the equation in standard form: x² − 9x − 6 = 0. Using the quadratic formula with a = 1, b = −9, and c = −6 gives x = (9 ± √(81 + 24))/2 = (9 ± √105)/2. These are the two values listed in choice C.

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