Step 1 :Isolate a square root on the left hand side : Original equation
4 = √-6-2x+√31-3x
Isolate
-√-6-2x = -4+√31-3x
Tidy up
√-6-2x = 4-√31-3x
Step 2 :Eliminate the radical on the left hand side : Raise both sides to the second power
(√-6-2x)2 = (4-√31-3x)2
After squaring
-6-2x = 31-3x+16-8√31-3x
Step 3 :Get remaining radical by itself : Current equation
-6-2x = 31-3x+16-8√31-3x
Isolate radical on the left hand side
8√31-3x = 6+2x+31-3x+16
Tidy up
8√31-3x = 53-x
Step 4 :Eliminate the radical on the left hand side : Raise both sides to the second power
(8√31-3x)2 = (53-x)2
After squaring
1984-192x = x2-106x+2809
Step 5 :Solve the quadratic equation : Rearranged equation
x2 + 86x + 825 = 0
This equation has two rational roots:
{x1, x2}={-11, -75}
Step 6 :Check that the first solution is correct : Original equation, root isolated, after tidy up
√-6-2x = 4-√31-3x
Plug in -11 for x
√-6-2•(-11) = 4-√31-3•(-11)
Simplify
√16 = -4
Solution does not check
4 ≠ -4
Step 7 :Check that the second solution is correct : Original equation, root isolated, after tidy up
√-6-2x = 4-√31-3x
Plug in -75 for x
√-6-2•(-75) = 4-√31-3•(-75)
Simplify
√144 = -12
Solution does not check
12 ≠ -12 Hopefully this helped You