x^2=1.2-3.3x

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Solution for x^2=1.2-3.3x equation: 


Simplifying
x2 = 1.2 + -3.3x

Solving
x2 = 1.2 + -3.3x

Solving for variable 'x'.

Reorder the terms:
-1.2 + 3.3x + x2 = 1.2 + -3.3x + -1.2 + 3.3x

Reorder the terms:
-1.2 + 3.3x + x2 = 1.2 + -1.2 + -3.3x + 3.3x

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + 3.3x + x2 = 0.0 + -3.3x + 3.3x
-1.2 + 3.3x + x2 = -3.3x + 3.3x

Combine like terms: -3.3x + 3.3x = 0.0
-1.2 + 3.3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 3.3x + 1.2 + x2 = 0.0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 3.3x + x2 = 0.0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 3.3x + x2 = 0.0 + 1.2
3.3x + x2 = 0.0 + 1.2

Combine like terms: 0.0 + 1.2 = 1.2
3.3x + x2 = 1.2

The x term is 3.3x.  Take half its coefficient (1.65).
Square it (2.7225) and add it to both sides.

Add '2.7225' to each side of the equation.
3.3x + 2.7225 + x2 = 1.2 + 2.7225

Reorder the terms:
2.7225 + 3.3x + x2 = 1.2 + 2.7225

Combine like terms: 1.2 + 2.7225 = 3.9225
2.7225 + 3.3x + x2 = 3.9225

Factor a perfect square on the left side:
(x + 1.65)(x + 1.65) = 3.9225

Calculate the square root of the right side: 1.980530232

Break this problem into two subproblems by setting 
(x + 1.65) equal to 1.980530232 and -1.980530232.


Subproblem 1
x + 1.65 = 1.980530232

Simplifying
x + 1.65 = 1.980530232

Reorder the terms:
1.65 + x = 1.980530232

Solving
1.65 + x = 1.980530232

Solving for variable 'x'.

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

Add '-1.65' to each side of the equation.
1.65 + -1.65 + x = 1.980530232 + -1.65

Combine like terms: 1.65 + -1.65 = 0.00
0.00 + x = 1.980530232 + -1.65
x = 1.980530232 + -1.65

Combine like terms: 1.980530232 + -1.65 = 0.330530232
x = 0.330530232

Simplifying
x = 0.330530232


Subproblem 2
x + 1.65 = -1.980530232

Simplifying
x + 1.65 = -1.980530232

Reorder the terms:
1.65 + x = -1.980530232

Solving
1.65 + x = -1.980530232

Solving for variable 'x'.

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

Add '-1.65' to each side of the equation.
1.65 + -1.65 + x = -1.980530232 + -1.65

Combine like terms: 1.65 + -1.65 = 0.00
0.00 + x = -1.980530232 + -1.65
x = -1.980530232 + -1.65

Combine like terms: -1.980530232 + -1.65 = -3.630530232
x = -3.630530232

Simplifying
x = -3.630530232


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.330530232, -3.630530232}

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