Question 752499
<pre>

  -3&#8730;<span style="text-decoration: overline">2x+1</span> + 5 = -4

We want to isolate the radical term -3&#8730;<span style="text-decoration: overline">2x+1</span> on the left.

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

      -3&#8730;<span style="text-decoration: overline">2x+1</span> = -9

We square both sides:

   (-3&#8730;<span style="text-decoration: overline">2x+1</span>)² = (-9)²

(-3)²(&#8730;<span style="text-decoration: overline">2x+1</span>)² = 81

      9(2x+1) = 81

        18x+9 = 81

          18x = 72

            x = {{{72/18}}}

            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&#8730;<span style="text-decoration: overline">2x+1</span> + 5 = -4

-3&#8730;<span style="text-decoration: overline">2(4)+1</span> + 5 = -4

   -3&#8730;<span style="text-decoration: overline">8+1</span> + 5 = -4

     -3&#8730;<span style="text-decoration: overline">9</span> + 5 = -4

    -3(3) + 5 = -4

       -9 + 5 = -4

           -4 = -4

So it checks.  The solution is 4

Edwin</pre>