(2x+1)2=4x(x-2)+13

Solution for (2x+1)2=4x(x-2)+13 equation:

Simplifying
(2x + 1) * 2 = 4x(x + -2) + 13

Reorder the terms:
(1 + 2x) * 2 = 4x(x + -2) + 13

Reorder the terms for easier multiplication:
2(1 + 2x) = 4x(x + -2) + 13
(1 * 2 + 2x * 2) = 4x(x + -2) + 13
(2 + 4x) = 4x(x + -2) + 13

Reorder the terms:
2 + 4x = 4x(-2 + x) + 13
2 + 4x = (-2 * 4x + x * 4x) + 13
2 + 4x = (-8x + 4x2) + 13

Reorder the terms:
2 + 4x = 13 + -8x + 4x2

Solving
2 + 4x = 13 + -8x + 4x2

Solving for variable 'x'.

Reorder the terms:
2 + -13 + 4x + 8x + -4x2 = 13 + -8x + 4x2 + -13 + 8x + -4x2

Combine like terms: 2 + -13 = -11
-11 + 4x + 8x + -4x2 = 13 + -8x + 4x2 + -13 + 8x + -4x2

Combine like terms: 4x + 8x = 12x
-11 + 12x + -4x2 = 13 + -8x + 4x2 + -13 + 8x + -4x2

Reorder the terms:
-11 + 12x + -4x2 = 13 + -13 + -8x + 8x + 4x2 + -4x2

Combine like terms: 13 + -13 = 0
-11 + 12x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
-11 + 12x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
-11 + 12x + -4x2 = 0 + 4x2 + -4x2
-11 + 12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-11 + 12x + -4x2 = 0

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

Divide each side by '-4'.
2.75 + -3x + x2 = 0

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + -3x + -2.75 + x2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + -3x + x2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + -3x + x2 = 0 + -2.75
-3x + x2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
-3x + x2 = -2.75

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -2.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -2.75 + 2.25

Combine like terms: -2.75 + 2.25 = -0.5
2.25 + -3x + x2 = -0.5

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.