CPM Homework Help : GB8I Problem 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.

$\array{(x+4)^2-2x-5=(x-1)^2\\ x^2+16-2x-5=x^2+1\\ 16-2x-5=1\\ \quad \ \ \ 11-2x=1\\ \qquad \qquad -2x=-10\\ \qquad \qquad x=5}$

Hint:

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

More Help:

You can tell if your answer is correct if you substitute it back into the original equation and obtain a true result.