How do you solve x+1=(x+1)^2?

1 Answer
sente
Jul 8, 2016

x in {-1,0}

Explanation:

We could expand the right hand side, gather all the terms on one side, and then solve the resulting quadratic, however because everything is currently in terms of x+1, let's use another approach.

Let u = x+1

Then we have

u = u^2

=> u^2-u = 0

=> u(u-1) = 0

=> u = 0 or u-1 = 0

=> x+1 = 0 or x+1-1 = 0

:. x = -1 or x = 0

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