Take \(x=-\frac{1}{2}\). It solves \[2x+1=0.\] Add \(x^2\) to both sides of the above equation \[x^2 + 2x +1 = x^2.\] Completing the square, we rewrite the equality as \[(x+1)^2 = x^2.\] Now, taking the square root from the both sides of the equality we get \[x+1=x.\] Subtracting \(x\) from both sides we get \[1=0\] Can you explain what went wrong in our reasoning? Why?