3x^2+12x+x^2-2x=-2x+4

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Solution for 3x^2+12x+x^2-2x=-2x+4 equation: 


Simplifying
3x2 + 12x + x2 + -2x = -2x + 4

Reorder the terms:
12x + -2x + 3x2 + x2 = -2x + 4

Combine like terms: 12x + -2x = 10x
10x + 3x2 + x2 = -2x + 4

Combine like terms: 3x2 + x2 = 4x2
10x + 4x2 = -2x + 4

Reorder the terms:
10x + 4x2 = 4 + -2x

Solving
10x + 4x2 = 4 + -2x

Solving for variable 'x'.

Reorder the terms:
-4 + 10x + 2x + 4x2 = 4 + -2x + -4 + 2x

Combine like terms: 10x + 2x = 12x
-4 + 12x + 4x2 = 4 + -2x + -4 + 2x

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

Combine like terms: 4 + -4 = 0
-4 + 12x + 4x2 = 0 + -2x + 2x
-4 + 12x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-4 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 3x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 3x + x2 = 0

Solving
-1 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 3x + x2 = 0 + 1

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

Combine like terms: 0 + 1 = 1
3x + x2 = 1

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 = 1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + 3x + x2 = 3.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 1.5 = 1.802775638

Simplifying
x + 1.5 = 1.802775638

Reorder the terms:
1.5 + x = 1.802775638

Solving
1.5 + x = 1.802775638

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 = 1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.802775638 + -1.5
x = 1.802775638 + -1.5

Combine like terms: 1.802775638 + -1.5 = 0.302775638
x = 0.302775638

Simplifying
x = 0.302775638


Subproblem 2
x + 1.5 = -1.802775638

Simplifying
x + 1.5 = -1.802775638

Reorder the terms:
1.5 + x = -1.802775638

Solving
1.5 + x = -1.802775638

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 = -1.802775638 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.802775638 + -1.5
x = -1.802775638 + -1.5

Combine like terms: -1.802775638 + -1.5 = -3.302775638
x = -3.302775638

Simplifying
x = -3.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.302775638, -3.302775638}
Solution
x = {0.302775638, -3.302775638}

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