SOLUTION: Solve equation. Check results. √(x-2) = x-4

Algebra ->  Radicals -> SOLUTION: Solve equation. Check results. √(x-2) = x-4      Log On


   

Question 427363: Solve equation. Check results.
√(x-2) = x-4
Found 2 solutions by ewatrrr, John10:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

sqrt%28x-2%29+=+x-4%29   |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) About Me  (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