(2x+1)(2x+1)-x=0

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Solution for (2x+1)(2x+1)-x=0 equation: 


Simplifying
(2x + 1)(2x + 1) + -1x = 0

Reorder the terms:
(1 + 2x)(2x + 1) + -1x = 0

Reorder the terms:
(1 + 2x)(1 + 2x) + -1x = 0

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -1x = 0
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -1x = 0
((1 + 2x) + 2x * (1 + 2x)) + -1x = 0
(1 + 2x + (1 * 2x + 2x * 2x)) + -1x = 0
(1 + 2x + (2x + 4x2)) + -1x = 0

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

Reorder the terms:
1 + 4x + -1x + 4x2 = 0

Combine like terms: 4x + -1x = 3x
1 + 3x + 4x2 = 0

Solving
1 + 3x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 0.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 0.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 0.75x + x2 = 0 + -0.25
0.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
0.75x + x2 = -0.25

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + 0.75x + x2 = -0.109375

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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