Question

Solve q - 6 = the square root of 27 - 2q

Answer 1

The answer and the procedure of working out can be seen in the picture

Answer 2

q - 6 = √(27 - 2q)
----------------------- each side squared by two
(q - 6)² = 27 - 2q
q² - 6q - 6q + 36 = 27 - 2q
q² - 12q + 36 = 27 - 2q
------------------------ move all terms to the left side
q² - 12q + 2q + 36 - 27 = 0
q² - 10q + 9 = 0
------------------------ factorize
(q - 9)(q - 1) = 0
q = 9 or q = 1

The solution is
q = 9
or
q = 1