Question Solve for x: sqrt (2x+11)-11=-8 Answer Attemptiout of 3 x=square

To solve the equation \(\sqrt{2x+11} - 11 = -8\), follow these steps:<br /><br />1. Isolate the square root term:<br /> \[<br /> \sqrt{2x+11} - 11 = -8<br /> \]<br /> Add 11 to both sides:<br /> \[<br /> \sqrt{2x+11} = 3<br /> \]<br /><br />2. Square both sides to eliminate the square root:<br /> \[<br /> (\sqrt{2x+11})^2 = 3^2<br /> \]<br /> Simplify:<br /> \[<br /> 2x + 11 = 9<br /> \]<br /><br />3. Solve for \(x\):<br /> Subtract 11 from both sides:<br /> \[<br /> 2x = 9 - 11<br /> \]<br /> Simplify:<br /> \[<br /> 2x = -2<br /> \]<br /> Divide both sides by 2:<br /> \[<br /> x = -1<br /> \]<br /><br />4. Verify the solution by substituting \(x = -1\) back into the original equation:<br /> \[<br /> \sqrt{2(-1) + 11} - 11 = -8<br /> \]<br /> Simplify inside the square root:<br /> \[<br /> \sqrt{-2 + 11} - 11 = -8<br /> \]<br /> \[<br /> \sqrt{9} - 11 = -8<br /> \]<br /> \[<br /> 3 - 11 = -8<br /> \]<br /> \[<br /> -8 = -8<br /> \]<br /><br />The solution \(x = -1\) is correct. Therefore, the final answer is:<br />\[<br />x = -1<br />\]