2x(x-1)=2+2(x+3)

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Solution for 2x(x-1)=2+2(x+3) equation: 


Simplifying
2x(x + -1) = 2 + 2(x + 3)

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

Reorder the terms:
-2x + 2x2 = 2 + 2(3 + x)
-2x + 2x2 = 2 + (3 * 2 + x * 2)
-2x + 2x2 = 2 + (6 + 2x)

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

Solving
-2x + 2x2 = 8 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + -2x + -2x + 2x2 = 8 + 2x + -8 + -2x

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -2x + x2 = 0

Solving
-4 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2x + x2 = 0 + 4

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

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

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 = 4 + 1

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

Combine like terms: 4 + 1 = 5
1 + -2x + x2 = 5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -1) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + -1 = 2.236067978

Simplifying
x + -1 = 2.236067978

Reorder the terms:
-1 + x = 2.236067978

Solving
-1 + x = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.236067978 + 1
x = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
x = 3.236067978

Simplifying
x = 3.236067978


Subproblem 2
x + -1 = -2.236067978

Simplifying
x + -1 = -2.236067978

Reorder the terms:
-1 + x = -2.236067978

Solving
-1 + x = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.236067978 + 1
x = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
x = -1.236067978

Simplifying
x = -1.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.236067978, -1.236067978}
Solution
x = {3.236067978, -1.236067978}

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