Answer:
6 is a solution, -4 is extraneous
Step-by-step explanation:
x = sqrt(2x+24)
square each side
x^2 =( sqrt(2x+24))^2
x^2 = 2x+24
Subtract 2x from each side
x^2 -2x = 2x-2x+24
x^2 -2x =24
Subtract 24 from each side
x^2 -2x-24 = 24-24
x^2 -2x-24 =0
Factor
(x-6) (x+4) =0
Using the zero product property
x=6 x=-4
Check the solutions in the original equation
x=6
6 = sqrt(2*6+24)
6 = sqrt(12+24)
6 = sqrt(36)
6=6
x=-4
-4 = sqrt(2*-4+24)
-4 = sqrt(-8+24)
-4 = sqrt(16)
-4=4 not a solution
