Solve the following: 2-sqrt (x+2)=3 For multiple solutions, separate your answers by a comma. If there are no solutions, write NONE.

We are tasked with solving the equation:<br /><br />\[<br />2 - \sqrt{x + 2} = 3<br />\]<br /><br />### Step 1: Isolate the square root term<br />Subtract \(2\) from both sides of the equation to isolate the square root term:<br /><br />\[<br />-\sqrt{x + 2} = 3 - 2<br />\]<br /><br />\[<br />-\sqrt{x + 2} = 1<br />\]<br /><br />### Step 2: Eliminate the negative sign<br />Multiply through by \(-1\) to remove the negative sign:<br /><br />\[<br />\sqrt{x + 2} = -1<br />\]<br /><br />### Step 3: Analyze the square root<br />The square root of a number cannot be negative. Therefore, the equation \(\sqrt{x + 2} = -1\) has **no solutions**.<br /><br />### Final Answer:<br />\[<br />\boxed{\text{NONE}}<br />\]