Solve for \( x \). Enter the solutions from least to greatest. Round to two decimal places. \( (x+7)^{2}-11=0 \) lesser \( x=\square \) greater \( x=\square \)

To solve the equation \( (x+7)^{2}-11=0 \), we first isolate the squared term: \[ (x+7)^{2} = 11 \] Next, we take the square root of both sides: \[ x+7 = \pm\sqrt{11} \] This gives us two equations to solve: 1. \( x + 7 = \sqrt{11} \) 2. \( x + 7 = -\sqrt{11} \) For the first equation: \[ x = \sqrt{11} - 7 \] Calculating \( \sqrt{11} \) gives approximately \( 3.32 \): \[ x \approx 3.32 - 7 = -3.68 \] For the second equation: \[ x = -\sqrt{11} - 7 \] This gives us: \[ x \approx -3.32 - 7 = -10.32 \] Now rounding both solutions to two decimal places, we find: Lesser \( x = -10.32 \) Greater \( x = -3.68 \)