12-4x+0.6x^2=11.3

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Solution for 12-4x+0.6x^2=11.3 equation: 


Simplifying
12 + -4x + 0.6x2 = 11.3

Solving
12 + -4x + 0.6x2 = 11.3

Solving for variable 'x'.

Reorder the terms:
12 + -11.3 + -4x + 0.6x2 = 11.3 + -11.3

Combine like terms: 12 + -11.3 = 0.7
0.7 + -4x + 0.6x2 = 11.3 + -11.3

Combine like terms: 11.3 + -11.3 = 0.0
0.7 + -4x + 0.6x2 = 0.0

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

Divide each side by '0.6'.
1.166666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -6.666666667x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -6.666666667x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -1.166666667
-6.666666667x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-6.666666667x + x2 = -1.166666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -1.166666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -1.166666667 + 11.11111112

Combine like terms: -1.166666667 + 11.11111112 = 9.944444453
11.11111112 + -6.666666667x + x2 = 9.944444453

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 9.944444453

Calculate the square root of the right side: 3.153481323

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.153481323 and -3.153481323.


Subproblem 1
x + -3.333333334 = 3.153481323

Simplifying
x + -3.333333334 = 3.153481323

Reorder the terms:
-3.333333334 + x = 3.153481323

Solving
-3.333333334 + x = 3.153481323

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.153481323 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.153481323 + 3.333333334
x = 3.153481323 + 3.333333334

Combine like terms: 3.153481323 + 3.333333334 = 6.486814657
x = 6.486814657

Simplifying
x = 6.486814657


Subproblem 2
x + -3.333333334 = -3.153481323

Simplifying
x + -3.333333334 = -3.153481323

Reorder the terms:
-3.333333334 + x = -3.153481323

Solving
-3.333333334 + x = -3.153481323

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.153481323 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.153481323 + 3.333333334
x = -3.153481323 + 3.333333334

Combine like terms: -3.153481323 + 3.333333334 = 0.179852011
x = 0.179852011

Simplifying
x = 0.179852011


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.486814657, 0.179852011}

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