x(x+2)=(x+1)2

Solution for x(x+2)=(x+1)2 equation:

Simplifying
x(x + 2) = (x + 1) * 2

Reorder the terms:
x(2 + x) = (x + 1) * 2
(2 * x + x * x) = (x + 1) * 2
(2x + x2) = (x + 1) * 2

Reorder the terms:
2x + x2 = (1 + x) * 2

Reorder the terms for easier multiplication:
2x + x2 = 2(1 + x)
2x + x2 = (1 * 2 + x * 2)
2x + x2 = (2 + 2x)

Add '-2x' to each side of the equation.
2x + -2x + x2 = 2 + 2x + -2x

Combine like terms: 2x + -2x = 0
0 + x2 = 2 + 2x + -2x
x2 = 2 + 2x + -2x

Combine like terms: 2x + -2x = 0
x2 = 2 + 0
x2 = 2

Solving
x2 = 2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}