3.6x^2-13.8x+9.2=0

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Solution for 3.6x^2-13.8x+9.2=0 equation: 


Simplifying
3.6x2 + -13.8x + 9.2 = 0

Reorder the terms:
9.2 + -13.8x + 3.6x2 = 0

Solving
9.2 + -13.8x + 3.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.6'.
2.555555556 + -3.833333333x + x2 = 0

Move the constant term to the right:

Add '-2.555555556' to each side of the equation.
2.555555556 + -3.833333333x + -2.555555556 + x2 = 0 + -2.555555556

Reorder the terms:
2.555555556 + -2.555555556 + -3.833333333x + x2 = 0 + -2.555555556

Combine like terms: 2.555555556 + -2.555555556 = 0.000000000
0.000000000 + -3.833333333x + x2 = 0 + -2.555555556
-3.833333333x + x2 = 0 + -2.555555556

Combine like terms: 0 + -2.555555556 = -2.555555556
-3.833333333x + x2 = -2.555555556

The x term is -3.833333333x.  Take half its coefficient (-1.916666667).
Square it (3.673611112) and add it to both sides.

Add '3.673611112' to each side of the equation.
-3.833333333x + 3.673611112 + x2 = -2.555555556 + 3.673611112

Reorder the terms:
3.673611112 + -3.833333333x + x2 = -2.555555556 + 3.673611112

Combine like terms: -2.555555556 + 3.673611112 = 1.118055556
3.673611112 + -3.833333333x + x2 = 1.118055556

Factor a perfect square on the left side:
(x + -1.916666667)(x + -1.916666667) = 1.118055556

Calculate the square root of the right side: 1.057381462

Break this problem into two subproblems by setting 
(x + -1.916666667) equal to 1.057381462 and -1.057381462.


Subproblem 1
x + -1.916666667 = 1.057381462

Simplifying
x + -1.916666667 = 1.057381462

Reorder the terms:
-1.916666667 + x = 1.057381462

Solving
-1.916666667 + x = 1.057381462

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = 1.057381462 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = 1.057381462 + 1.916666667
x = 1.057381462 + 1.916666667

Combine like terms: 1.057381462 + 1.916666667 = 2.974048129
x = 2.974048129

Simplifying
x = 2.974048129


Subproblem 2
x + -1.916666667 = -1.057381462

Simplifying
x + -1.916666667 = -1.057381462

Reorder the terms:
-1.916666667 + x = -1.057381462

Solving
-1.916666667 + x = -1.057381462

Solving for variable 'x'.

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

Add '1.916666667' to each side of the equation.
-1.916666667 + 1.916666667 + x = -1.057381462 + 1.916666667

Combine like terms: -1.916666667 + 1.916666667 = 0.000000000
0.000000000 + x = -1.057381462 + 1.916666667
x = -1.057381462 + 1.916666667

Combine like terms: -1.057381462 + 1.916666667 = 0.859285205
x = 0.859285205

Simplifying
x = 0.859285205


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.974048129, 0.859285205}

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