-3√2x+1 + 5 = -4

We want to isolate the radical term -3√2x+1 on the left.

So we add -5 to both sides to get rid of the +5 on the left

      -3√2x+1 = -9

We square both sides:

   (-3√2x+1)² = (-9)²

(-3)²(√2x+1)² = 81

      9(2x+1) = 81

        18x+9 = 81

          18x = 72

            x = 

            x = 4 

We MUST ALWAYS check radical equations,
because when you square both sides of
an equation, you would get the same
equation whether what was squared was
positive or negative.  So you may get
phony solutions, called "extraneous
solutions". 
 
  -3√2x+1 + 5 = -4

-3√2(4)+1 + 5 = -4

   -3√8+1 + 5 = -4

     -3√9 + 5 = -4

    -3(3) + 5 = -4

       -9 + 5 = -4

           -4 = -4

So it checks.  The solution is 4

Edwin