Solve the radical equation. Check all proposed solutions.
\[
x-\sqrt{4 x-15}=5
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is (Use a comma to separate answers as needed. Simplify your answer.)
B. The solution set is $\varnothing$.
Answer
Final Answer: The solution set is \(\boxed{4, 10}\)
Step 1 ：Isolate the radical on one side of the equation: \(x = 5 + \sqrt{4x - 15}\)
Step 2 ：Square both sides of the equation to eliminate the radical: \((x - 5)^2 = 4x - 15\)
Step 3 ：Solve the resulting quadratic equation to get the proposed solutions: \(x = 4, 10\)
Step 4 ：Check the proposed solutions in the original equation: \(4 - \sqrt{4*4 - 15} = 5\) and \(10 - \sqrt{4*10 - 15} = 5\)
Step 5 ：Both proposed solutions are valid.
Step 6 ：Final Answer: The solution set is \(\boxed{4, 10}\)
