### Home > CCA > Chapter 5 > Lesson 5.1.1 > Problem5-14

5-14.

Jackie and Alexa were working on homework together when Jackie said, “I got x = 5 as the solution, but it looks like you got something different. Which solution is right?”

I think you made a mistake,” said Alexa. Did Jackie make a mistake? Help Jackie figure out whether she made a mistake and, if she did, explain her mistake and show her how to solve the equation correctly. Jackie’s work is shown at right. Homework Help ✎

$\left. \begin{array}{l}{ ( x + 4 ) ^ { 2 } - 2 x - 5 = ( x - 1 ) ^ { 2 } }\\{ x ^ { 2 } + 16 - 2 x - 5 = x ^ { 2 } + 1 }\\{ 16 - 2 x - 5 = 1 }\\{ 11 - 2 x = 1 }\\{ - 2 x = - 10 }\\{ x = 5 }\end{array} \right.$

Remember that (x + 4)2 = (x + 4)(x + 4) and (x − 1)2 = (x − 1)(x − 1).