-(x^2+4x-4)=x+2x^2-4+(x)

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


Simplifying
-1(x2 + 4x + -4) = x + 2x2 + -4 + (x)

Reorder the terms:
-1(-4 + 4x + x2) = x + 2x2 + -4 + (x)
(-4 * -1 + 4x * -1 + x2 * -1) = x + 2x2 + -4 + (x)
(4 + -4x + -1x2) = x + 2x2 + -4 + (x)
4 + -4x + -1x2 = x + 2x2 + -4 + x

Reorder the terms:
4 + -4x + -1x2 = -4 + x + x + 2x2

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

Solving
4 + -4x + -1x2 = -4 + 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + 4 + -4x + -2x + -1x2 + -2x2 = -4 + 2x + 2x2 + 4 + -2x + -2x2

Combine like terms: 4 + 4 = 8
8 + -4x + -2x + -1x2 + -2x2 = -4 + 2x + 2x2 + 4 + -2x + -2x2

Combine like terms: -4x + -2x = -6x
8 + -6x + -1x2 + -2x2 = -4 + 2x + 2x2 + 4 + -2x + -2x2

Combine like terms: -1x2 + -2x2 = -3x2
8 + -6x + -3x2 = -4 + 2x + 2x2 + 4 + -2x + -2x2

Reorder the terms:
8 + -6x + -3x2 = -4 + 4 + 2x + -2x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
8 + -6x + -3x2 = 0 + 2x + -2x + 2x2 + -2x2
8 + -6x + -3x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
8 + -6x + -3x2 = 0 + 2x2 + -2x2
8 + -6x + -3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
8 + -6x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2.666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 2x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 2x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 2x + x2 = 0 + 2.666666667
2x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
2x + x2 = 2.666666667

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 = 2.666666667 + 1

Reorder the terms:
1 + 2x + x2 = 2.666666667 + 1

Combine like terms: 2.666666667 + 1 = 3.666666667
1 + 2x + x2 = 3.666666667

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(x + 1) equal to 1.914854216 and -1.914854216.

Subproblem 1

x + 1 = 1.914854216 Simplifying x + 1 = 1.914854216 Reorder the terms: 1 + x = 1.914854216 Solving 1 + x = 1.914854216 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 = 1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.914854216 + -1 x = 1.914854216 + -1 Combine like terms: 1.914854216 + -1 = 0.914854216 x = 0.914854216 Simplifying x = 0.914854216

Subproblem 2

x + 1 = -1.914854216 Simplifying x + 1 = -1.914854216 Reorder the terms: 1 + x = -1.914854216 Solving 1 + x = -1.914854216 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 = -1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.914854216 + -1 x = -1.914854216 + -1 Combine like terms: -1.914854216 + -1 = -2.914854216 x = -2.914854216 Simplifying x = -2.914854216

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.914854216, -2.914854216}

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