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Algebra Level 2

Which solution to the equation x2=xx^2 = x contains an error?


Original:                                                 x2=xDivide both sides by x:          x=1\begin{aligned} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Divide both sides by x:}\;\;\;\;\; x &= 1 \end{aligned}


Original:                                                                                                             x2=xSubtract x from both sides:                                        x2x=0Factor:                                                                                                x(x1)=0Use the Zero Product Property:                              x=0,x=1\begin{aligned} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Subtract x from both sides:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x^2 - x &= 0\\ \text{Factor:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x(x-1) &= 0\\ \text{Use the Zero Product Property:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x =0&, x = 1 \end{aligned}


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