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

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


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

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

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

Reorder the terms:
-2 + -3x = -2x(1 + x)
-2 + -3x = (1 * -2x + x * -2x)
-2 + -3x = (-2x + -2x2)

Solving
-2 + -3x = -2x + -2x2

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '2'.
-1 + -0.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.5x + x2 = 0 + 1
-0.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.5x + x2 = 1

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 1 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1 + 0.0625

Combine like terms: 1 + 0.0625 = 1.0625
0.0625 + -0.5x + x2 = 1.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -0.25 = 1.030776406 Simplifying x + -0.25 = 1.030776406 Reorder the terms: -0.25 + x = 1.030776406 Solving -0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.030776406 + 0.25 x = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 x = 1.280776406 Simplifying x = 1.280776406

Subproblem 2

x + -0.25 = -1.030776406 Simplifying x + -0.25 = -1.030776406 Reorder the terms: -0.25 + x = -1.030776406 Solving -0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.030776406 + 0.25 x = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 x = -0.780776406 Simplifying x = -0.780776406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.280776406, -0.780776406}

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