Factorise the equation first:

Find two numbers that multiply to give you 1, and add to give you 2:

Both numbers are 1, therefore

[math]x^2 + 2x + 1 = (x + 1)(x + 1) = (x + 1)^2[/math]

To solve, make the equation equal to 0:

[math](x + 1)(x + 1) = 0[/math]

Therefore our answer is [math]x = -1[/math]

We call this a repeated root.