2x-3x*x=4x+2

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Solution for 2x-3x*x=4x+2 equation:


Simplifying
2x + -3x * x = 4x + 2

Multiply x * x
2x + -3x2 = 4x + 2

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

Solving
2x + -3x2 = 2 + 4x

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 2x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(2 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 2x + 3x2 = 0

Solving
2 + 2x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.6666666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + -0.6666666667
0.6666666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.6666666667x + x2 = -0.6666666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -0.6666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -0.6666666667 + 0.1111111112

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + 0.6666666667x + x2 = -0.5555555555

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = -0.5555555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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