Solve the radical equation Check all proposed solutions Squa

Solve the radical equation. Check all proposed solutions Squareroot x + 8 = x + 2 Select the correct choice below and. if necessary, fill in the answer box to complete your choice the solution set is (Use a comma to separate answers as needed.) There is no solution.

Solution

(Sqrt x) +8=x+2

Sqrt x = x-6

Squaring both sides

x=(x-6)²

x=x²-12x+36

x²-13x+36=0

(x-4)(x-9)=0

x=4,9

Checking the solutions

Sqrt 4 +8= 4+2

2+8=4+2

10=6 which is not true.

Sqrt 9 + 8= 9+2

11=11 which is true. Hence the correct solution is x=9