Question 1 of 33
Solve $\sqrt{4 x+24}=x+3$. Check for extraneous solutions.
A. No solution
B. $x=-5$
C. $x=-5,3$
D. $x=3$

Answer

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Answer

Final Answer: The solution to the equation $\sqrt{4 x+24}=x+3$ is $\boxed{x=3}$.

Steps

Step 1 ：Square both sides of the equation to get rid of the square root, resulting in $4x + 24 = (x + 3)^2$.

Step 2 ：Simplify the equation to solve for x, resulting in $x^2 - 2x - 9 = 0$.

Step 3 ：Solve the equation to find the solution, which is $x = 3$.

Step 4 ：Substitute $x = 3$ back into the original equation to check for extraneous solutions. The original equation holds true, so $x = 3$ is not an extraneous solution.

Step 5 ：Final Answer: The solution to the equation $\sqrt{4 x+24}=x+3$ is $\boxed{x=3}$.

Question 1 of 33Solve $\sqrt{4 x+24}=x+3$. Check for extraneous solutions.A. No solutionB. $x=-5$C. $x=-5,3$D. $x=3$

Answer

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Question 1 of 33
Solve $\sqrt{4 x+24}=x+3$. Check for extraneous solutions.
A. No solution
B. $x=-5$
C. $x=-5,3$
D. $x=3$