5x^2+2x=-4x^2-4x+4

Solution for 5x^2+2x=-4x^2-4x+4 equation:

Simplifying
5x2 + 2x = -4x2 + -4x + 4

Reorder the terms:
2x + 5x2 = -4x2 + -4x + 4

Reorder the terms:
2x + 5x2 = 4 + -4x + -4x2

Solving
2x + 5x2 = 4 + -4x + -4x2

Solving for variable 'x'.

Reorder the terms:
-4 + 2x + 4x + 5x2 + 4x2 = 4 + -4x + -4x2 + -4 + 4x + 4x2

Combine like terms: 2x + 4x = 6x
-4 + 6x + 5x2 + 4x2 = 4 + -4x + -4x2 + -4 + 4x + 4x2

Combine like terms: 5x2 + 4x2 = 9x2
-4 + 6x + 9x2 = 4 + -4x + -4x2 + -4 + 4x + 4x2

Reorder the terms:
-4 + 6x + 9x2 = 4 + -4 + -4x + 4x + -4x2 + 4x2

Combine like terms: 4 + -4 = 0
-4 + 6x + 9x2 = 0 + -4x + 4x + -4x2 + 4x2
-4 + 6x + 9x2 = -4x + 4x + -4x2 + 4x2

Combine like terms: -4x + 4x = 0
-4 + 6x + 9x2 = 0 + -4x2 + 4x2
-4 + 6x + 9x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-4 + 6x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 0.6666666667x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 0.6666666667x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.4444444444
0.6666666667x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
0.6666666667x + x2 = 0.4444444444

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 = 0.4444444444 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.4444444444 + 0.1111111112

Combine like terms: 0.4444444444 + 0.1111111112 = 0.5555555556
0.1111111112 + 0.6666666667x + x2 = 0.5555555556

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.5555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.745355993 and -0.745355993.

Subproblem 1
x + 0.3333333334 = 0.745355993

Simplifying
x + 0.3333333334 = 0.745355993

Reorder the terms:
0.3333333334 + x = 0.745355993

Solving
0.3333333334 + x = 0.745355993

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.745355993 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.745355993 + -0.3333333334
x = 0.745355993 + -0.3333333334

Combine like terms: 0.745355993 + -0.3333333334 = 0.4120226596
x = 0.4120226596

Simplifying
x = 0.4120226596

Subproblem 2
x + 0.3333333334 = -0.745355993

Simplifying
x + 0.3333333334 = -0.745355993

Reorder the terms:
0.3333333334 + x = -0.745355993

Solving
0.3333333334 + x = -0.745355993

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.745355993 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.745355993 + -0.3333333334
x = -0.745355993 + -0.3333333334

Combine like terms: -0.745355993 + -0.3333333334 = -1.0786893264
x = -1.0786893264

Simplifying
x = -1.0786893264

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4120226596, -1.0786893264}