Hi

   |Squaring both sides of the Equation

    x-2 = x^2 - 8x + 16

   x^2 -9x + 18 = 0

factoring

 (x-3)(x-6) = 0 Note:SUM of the outside terms(-6x) and the inside terms(-3x) = -9x

 (x-3)= 0    x = 3  |Tossing out: sqrt(1) ≠ -1

 (x-6) = 0   x = 6

It is always recommended to 'check out' the solutions found in the original EQ 

Answer by John10(297)   (Show Source): You can put this solution on YOUR website!
 √(x-2) = x-4



Take square for both sides to eliminate the root on the left side



(√(x-2))^2 = (x-4)^2



(x - 2) = x^2 - 8x + 16



x^2 - 9x + 18 = 0



From here, we can use any methods to solve the quadratic equation



I will use A.C method to factoring the left side



(x - 6)(x - 3) =0



Apply the zero product property to let each binomial to be zero



x - 6 = 0 OR x - 3 = 0



x = 6 OR x = 3



Check your answer:



If x = 6 then the left side √(6-2)= √4 = 2 and the right side is 6 - 4 = 2



If x = 3  left side √(3-2)= √1 = 1 and the right side is 3 - 4 = -1



So the ONLY solution is x = 6



 

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