Can someone help me solve for x?

Question

5*√(x) - √(x-1) = 6

i am completely lost. thank you for any help.

Answer 1

Raise both sides of the equation to square.

After that bring all contant terms to one side, keep the radical on the other side.

Bring to square once more to remove the radical sign.

Solve the new equation for x.

Take only those solutions satisfying the condition x≥1 (so that √(x) and √(x-1) have a meaning)

Answer 2

Add √(x-1)  to both sides:

5√x=6+√(x-1)

Square both sides:

25x=36+2√(x-1) +(x-1)

25x=35+x+2√(x-1)

Get the radical all alone on one side

24x-35=2√(x-1)

Square both sides again

576x²-1680x+1225=4x-4

576x²-1684x+1229=0

Use quadratic formula from there.

_/

Answer 3

Square both sides

( (5√(x) - √(x-1) )^2 = (6)^2

25x - 10√(x)√(x-1) + x-1 = 36

26x - 37 = 10√(x)√(x-1)

square again

676x^2 - 1924x + 1369 = 100x^2 - 100x

576x^2 - 1824x +1369 = 0

and use quadratic formula from here

Answer 4

place your 6 on the other with a minus sign and then put that into yuor TI 84 at the (y =) plot 1 and play with the table until you find 6 on the y side. It should be--> X=8.74044.