52=(2x+1)(x+1)

Solution for 52=(2x+1)(x+1) equation:

Simplifying
52 = (2x + 1)(x + 1)

Reorder the terms:
52 = (1 + 2x)(x + 1)

Reorder the terms:
52 = (1 + 2x)(1 + x)

Multiply (1 + 2x) * (1 + x)
52 = (1(1 + x) + 2x * (1 + x))
52 = ((1 * 1 + x * 1) + 2x * (1 + x))
52 = ((1 + 1x) + 2x * (1 + x))
52 = (1 + 1x + (1 * 2x + x * 2x))
52 = (1 + 1x + (2x + 2x2))

Combine like terms: 1x + 2x = 3x
52 = (1 + 3x + 2x2)

Solving
52 = 1 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 52 + -1 = 51
51 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2

Reorder the terms:
51 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
51 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
51 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
51 + -3x + -2x2 = 0 + 2x2 + -2x2
51 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
51 + -3x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-25.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + 1.5x + 25.5 + x2 = 0 + 25.5

Reorder the terms:
-25.5 + 25.5 + 1.5x + x2 = 0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + 1.5x + x2 = 0 + 25.5
1.5x + x2 = 0 + 25.5

Combine like terms: 0 + 25.5 = 25.5
1.5x + x2 = 25.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 25.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 25.5 + 0.5625

Combine like terms: 25.5 + 0.5625 = 26.0625
0.5625 + 1.5x + x2 = 26.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 26.0625

Calculate the square root of the right side: 5.105144464

Break this problem into two subproblems by setting 
(x + 0.75) equal to 5.105144464 and -5.105144464.

Subproblem 1
x + 0.75 = 5.105144464

Simplifying
x + 0.75 = 5.105144464

Reorder the terms:
0.75 + x = 5.105144464

Solving
0.75 + x = 5.105144464

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 5.105144464 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 5.105144464 + -0.75
x = 5.105144464 + -0.75

Combine like terms: 5.105144464 + -0.75 = 4.355144464
x = 4.355144464

Simplifying
x = 4.355144464

Subproblem 2
x + 0.75 = -5.105144464

Simplifying
x + 0.75 = -5.105144464

Reorder the terms:
0.75 + x = -5.105144464

Solving
0.75 + x = -5.105144464

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -5.105144464 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -5.105144464 + -0.75
x = -5.105144464 + -0.75

Combine like terms: -5.105144464 + -0.75 = -5.855144464
x = -5.855144464

Simplifying
x = -5.855144464

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.355144464, -5.855144464}