Respuesta :

Answer:

The solution set is  = {7, 9}.

Step-by-step explanation:

√(6x - 38) = x - 5

Square both sides:

6x - 38 = (x - 5)^2

x^2 - 10x + 25 - 6x + 38 = 0

x^2 - 16x + 63 = 0

(x - 7)(x - 9) = 0

x = 7, 9.

Check these solutions:

x = 7:

√(6x - 38) = √(42-38)  = 2  and 7 - 5 = 2 so this is correct.

x = 9

√(6x - 38) = √(54 - 38) = √16 = 4  and 9 - 5 = 4 so 9 is also correct.
Answer:

{7, 9}

I hope this helps you!!