-(x+1)(x+1)=-27

Solution for -(x+1)(x+1)=-27 equation:

Simplifying
-1(x + 1)(x + 1) = -27

Reorder the terms:
-1(1 + x)(x + 1) = -27

Reorder the terms:
-1(1 + x)(1 + x) = -27

Multiply (1 + x) * (1 + x)
-1(1(1 + x) + x(1 + x)) = -27
-1((1 * 1 + x * 1) + x(1 + x)) = -27
-1((1 + 1x) + x(1 + x)) = -27
-1(1 + 1x + (1 * x + x * x)) = -27
-1(1 + 1x + (1x + x2)) = -27

Combine like terms: 1x + 1x = 2x
-1(1 + 2x + x2) = -27
(1 * -1 + 2x * -1 + x2 * -1) = -27
(-1 + -2x + -1x2) = -27

Solving
-1 + -2x + -1x2 = -27

Solving for variable 'x'.

Reorder the terms:
-1 + 27 + -2x + -1x2 = -27 + 27

Combine like terms: -1 + 27 = 26
26 + -2x + -1x2 = -27 + 27

Combine like terms: -27 + 27 = 0
26 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-26 + 2x + x2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 2x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2x + x2 = 0 + 26
2x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
2x + x2 = 26

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 26 + 1

Reorder the terms:
1 + 2x + x2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + 2x + x2 = 27

Factor a perfect square on the left side:
(x + 1)(x + 1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 1) equal to 5.196152423 and -5.196152423.

Subproblem 1
x + 1 = 5.196152423

Simplifying
x + 1 = 5.196152423

Reorder the terms:
1 + x = 5.196152423

Solving
1 + x = 5.196152423

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.196152423 + -1
x = 5.196152423 + -1

Combine like terms: 5.196152423 + -1 = 4.196152423
x = 4.196152423

Simplifying
x = 4.196152423

Subproblem 2
x + 1 = -5.196152423

Simplifying
x + 1 = -5.196152423

Reorder the terms:
1 + x = -5.196152423

Solving
1 + x = -5.196152423

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.196152423 + -1
x = -5.196152423 + -1

Combine like terms: -5.196152423 + -1 = -6.196152423
x = -6.196152423

Simplifying
x = -6.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.196152423, -6.196152423}