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 $\emptyset$ .

Answer

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Answer

Final Answer: The solution set is $4, 10$

Steps

Step 1 ：Isolate the radical on one side of the equation: $x = 5 + \sqrt{4 x - 15}$

Step 2 ：Square both sides of the equation to eliminate the radical: $(x - 5)^{2} = 4 x - 15$

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 $4, 10$