Solve and check your solution(s). If the equation has no real solution, so state.
-
A) 2
B) -1
C) 2, -1
D) no real solution

Question

Solve and check your solution(s). If the equation has no real solution, so state.
-
A) 2 
B) -1 
C) 2, -1 
D) no real solution

Quizplus · Accepted Answer

To solve the equation, we can start by taking the square root of both sides:

sqrt(5x - 1) - 3 = x

Then, we can isolate the radical term on one side:

sqrt(5x - 1) = x + 3

Squaring both sides eliminates the radical:

5x - 1 = x^2 + 6x + 9

Rearranging and simplifying:

x^2 + x - 10 = 0

Now we can factor:

(x + 2)(x - 5) = 0

Therefore, x = -2 or x = 5.

However, we must check for extraneous solutions by plugging both values back into the original equation: 
For x = -2: sqrt(5(-2) - 1) - 3 = -2 
sqrt(-11) - 3 = -2 
There is no real solution for this part.

For x = 5: sqrt(5(5) - 1) - 3 = 5 
sqrt(24) - 3 = 5 
sqrt(24) = 8 
8^2 = 24 + 1 
25 = 25

Therefore, the only solution that works is x = 5, and the answer is A) 2.

Solve and Check Your Solution(s)