What is x^2 + (x + 1^2) = ( x + 2^2)?

1² = 1 and 2² = 4

The parentheses are not necessary as there is no factor.

x² + x + 1 = x + 4 | -x
x² + 1 = 4 | - 1
x² = 3 | sqrt()
x1 = sqrt(3)
x2 = -sqrt(3)

Note that -sqrt(3) is not to be mixed up with sqrt(-3).

"sqrt" means square root.