Answer: x=6.7016 I hope this will help
Step-by-step explanation: STEP 1.
Isolate the square root on the left hand side
Radical already isolated
√5x-1 = x-1
STEP 2.
Eliminate the radical on the left hand side
Raise both sides to the second power
(√5x-1)2 = (x-1)2
After squaring
5x-1 = x2-2x+1STEP
Step 3.
Solve the quadratic equation
Rearranged equation
x2 - 7x + 2 = 0
This equation has two real roots:
x1 = ( 7 + sqrt( 41) ) / 2 = 6.7016
x2 = ( 7 - sqrt( 41) ) / 2 = 0.2984STEP
Step 4.
Check that the first solution is correct
Original equation
√5x-1 = x-1
Plug in 6.7016 for x
√5•( 6.7016) -1 = ( 6.7016) -1
Simplify
√32.508 = 5.702
Solution checks !!
Solution is:
x = 6.7016 STEP
Step 5.
Check that the second solution is correct
Original equation
√5x-1 = x-1
Plug in 0.2984 for x
√5•( 0.2984) -1 = ( 0.2984) -1
Simplify
√0.492 = -0.702
Solution does not check
0.702 ≠ -0.702
