12-1x(x+1)=-2(2-x)

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Solution for 12-1x(x+1)=-2(2-x) equation: 


Simplifying
12 + -1x(x + 1) = -2(2 + -1x)

Reorder the terms:
12 + -1x(1 + x) = -2(2 + -1x)
12 + (1 * -1x + x * -1x) = -2(2 + -1x)
12 + (-1x + -1x2) = -2(2 + -1x)
12 + -1x + -1x2 = (2 * -2 + -1x * -2)
12 + -1x + -1x2 = (-4 + 2x)

Solving
12 + -1x + -1x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
12 + 4 + -1x + -2x + -1x2 = -4 + 2x + 4 + -2x

Combine like terms: 12 + 4 = 16
16 + -1x + -2x + -1x2 = -4 + 2x + 4 + -2x

Combine like terms: -1x + -2x = -3x
16 + -3x + -1x2 = -4 + 2x + 4 + -2x

Reorder the terms:
16 + -3x + -1x2 = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
16 + -3x + -1x2 = 0 + 2x + -2x
16 + -3x + -1x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
16 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 3x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 3x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3x + x2 = 0 + 16
3x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
3x + x2 = 16

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 = 16 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3x + x2 = 18.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
x + 1.5 = 4.272001873

Simplifying
x + 1.5 = 4.272001873

Reorder the terms:
1.5 + x = 4.272001873

Solving
1.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.272001873 + -1.5
x = 4.272001873 + -1.5

Combine like terms: 4.272001873 + -1.5 = 2.772001873
x = 2.772001873

Simplifying
x = 2.772001873


Subproblem 2
x + 1.5 = -4.272001873

Simplifying
x + 1.5 = -4.272001873

Reorder the terms:
1.5 + x = -4.272001873

Solving
1.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.272001873 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.272001873 + -1.5
x = -4.272001873 + -1.5

Combine like terms: -4.272001873 + -1.5 = -5.772001873
x = -5.772001873

Simplifying
x = -5.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.772001873, -5.772001873}

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