I am hoping this was explained well enough:
Step 1 :
Isolate the square root on the left hand side :
Radical already isolated
√2x-7 = 5-x
Step 2 :
Eliminate the radical on the left hand side :
Raise both sides to the second power
(√2x-7)2 = (5-x)2
After squaring
2x-7 = x2-10x+25
Step 3 :
Solve the quadratic equation :
Rearranged equation
x2 - 12x + 32 = 0
This equation has two rational roots:
{x1, x2}={8, 4}
Step 4 :
Check that the first solution is correct :
Original equation
√2x-7 = 5-x
Plug in 8 for x
√2•(8)-7 = 5-(8)
Simplify
√9 = -3
Solution does not check
3 ≠ -3
Step 5 :
Check that the second solution is correct :
Original equation
√2x-7 = 5-x
Plug in 4 for x
√2•(4)-7 = 5-(4)
Simplify
√1 = 1
Solution checks !!
Solution is:
x = 4
One solution was found :
x = 4