-6x^2+4x+7=-3x^2-3x+2

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Solution for -6x^2+4x+7=-3x^2-3x+2 equation: 


Simplifying
-6x2 + 4x + 7 = -3x2 + -3x + 2

Reorder the terms:
7 + 4x + -6x2 = -3x2 + -3x + 2

Reorder the terms:
7 + 4x + -6x2 = 2 + -3x + -3x2

Solving
7 + 4x + -6x2 = 2 + -3x + -3x2

Solving for variable 'x'.

Reorder the terms:
7 + -2 + 4x + 3x + -6x2 + 3x2 = 2 + -3x + -3x2 + -2 + 3x + 3x2

Combine like terms: 7 + -2 = 5
5 + 4x + 3x + -6x2 + 3x2 = 2 + -3x + -3x2 + -2 + 3x + 3x2

Combine like terms: 4x + 3x = 7x
5 + 7x + -6x2 + 3x2 = 2 + -3x + -3x2 + -2 + 3x + 3x2

Combine like terms: -6x2 + 3x2 = -3x2
5 + 7x + -3x2 = 2 + -3x + -3x2 + -2 + 3x + 3x2

Reorder the terms:
5 + 7x + -3x2 = 2 + -2 + -3x + 3x + -3x2 + 3x2

Combine like terms: 2 + -2 = 0
5 + 7x + -3x2 = 0 + -3x + 3x + -3x2 + 3x2
5 + 7x + -3x2 = -3x + 3x + -3x2 + 3x2

Combine like terms: -3x + 3x = 0
5 + 7x + -3x2 = 0 + -3x2 + 3x2
5 + 7x + -3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
5 + 7x + -3x2 = 0

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

Divide each side by '-3'.
-1.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2.333333333x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2.333333333x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 1.666666667
-2.333333333x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2.333333333x + x2 = 1.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 1.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 1.666666667 + 1.361111112

Combine like terms: 1.666666667 + 1.361111112 = 3.027777779
1.361111112 + -2.333333333x + x2 = 3.027777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 3.027777779

Calculate the square root of the right side: 1.740051085

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.740051085 and -1.740051085.


Subproblem 1
x + -1.166666667 = 1.740051085

Simplifying
x + -1.166666667 = 1.740051085

Reorder the terms:
-1.166666667 + x = 1.740051085

Solving
-1.166666667 + x = 1.740051085

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.740051085 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.740051085 + 1.166666667
x = 1.740051085 + 1.166666667

Combine like terms: 1.740051085 + 1.166666667 = 2.906717752
x = 2.906717752

Simplifying
x = 2.906717752


Subproblem 2
x + -1.166666667 = -1.740051085

Simplifying
x + -1.166666667 = -1.740051085

Reorder the terms:
-1.166666667 + x = -1.740051085

Solving
-1.166666667 + x = -1.740051085

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.740051085 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.740051085 + 1.166666667
x = -1.740051085 + 1.166666667

Combine like terms: -1.740051085 + 1.166666667 = -0.573384418
x = -0.573384418

Simplifying
x = -0.573384418


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.906717752, -0.573384418}

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