Extraneous solution q-6 = square root 27-2q

q = 1, q = 9

Step-by-step explanation:

Equation: q - 6 = √ (27 - 2q)

Exponents: (q - 6) ² = 27 - 2q

Simplify: q² - 12q + 36 = 27 - 2q

Subtract: q² - 10q + 9 = 0

Two numbers: a + b = - 10, ab = 9 - -> a = - 1, b = - 9

Substitute: q² - 1q - 9q + 9 = 0

Simplify: (q - 1) (q - 9) = 0

Solve: q - 1 = 0, q - 9 = 0 - -> q = 1, q = 9