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

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

Simplifying
2(x + 1)(x + 1) = (2x2) + 1

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

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

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) = (2x2) + 1
2((1 * 1 + x * 1) + x(1 + x)) = (2x2) + 1
2((1 + 1x) + x(1 + x)) = (2x2) + 1
2(1 + 1x + (1 * x + x * x)) = (2x2) + 1
2(1 + 1x + (1x + x2)) = (2x2) + 1

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) = (2x2) + 1
(1 * 2 + 2x * 2 + x2 * 2) = (2x2) + 1
(2 + 4x + 2x2) = (2x2) + 1

Reorder the terms:
2 + 4x + 2x2 = 1 + (2x2)

Add '-2x2' to each side of the equation.
2 + 4x + 2x2 + -2x2 = 1 + (2x2) + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 4x + 0 = 1 + (2x2) + -2x2
2 + 4x = 1 + (2x2) + -2x2

Combine like terms: (2x2) + -2x2 = 0
2 + 4x = 1 + 0
2 + 4x = 1

Solving
2 + 4x = 1

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + 4x = 1 + -2

Combine like terms: 2 + -2 = 0
0 + 4x = 1 + -2
4x = 1 + -2

Combine like terms: 1 + -2 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25