1.2X-0.22X^2+1.01=0

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Solution for 1.2X-0.22X^2+1.01=0 equation: 


Simplifying
1.2X + -0.22X2 + 1.01 = 0

Reorder the terms:
1.01 + 1.2X + -0.22X2 = 0

Solving
1.01 + 1.2X + -0.22X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-0.22 the coefficient of the squared term: 

Divide each side by '-0.22'.
-4.590909091 + -5.454545455X + X2 = 0

Move the constant term to the right:

Add '4.590909091' to each side of the equation.
-4.590909091 + -5.454545455X + 4.590909091 + X2 = 0 + 4.590909091

Reorder the terms:
-4.590909091 + 4.590909091 + -5.454545455X + X2 = 0 + 4.590909091

Combine like terms: -4.590909091 + 4.590909091 = 0.000000000
0.000000000 + -5.454545455X + X2 = 0 + 4.590909091
-5.454545455X + X2 = 0 + 4.590909091

Combine like terms: 0 + 4.590909091 = 4.590909091
-5.454545455X + X2 = 4.590909091

The X term is -5.454545455X.  Take half its coefficient (-2.727272728).
Square it (7.438016533) and add it to both sides.

Add '7.438016533' to each side of the equation.
-5.454545455X + 7.438016533 + X2 = 4.590909091 + 7.438016533

Reorder the terms:
7.438016533 + -5.454545455X + X2 = 4.590909091 + 7.438016533

Combine like terms: 4.590909091 + 7.438016533 = 12.028925624
7.438016533 + -5.454545455X + X2 = 12.028925624

Factor a perfect square on the left side:
(X + -2.727272728)(X + -2.727272728) = 12.028925624

Calculate the square root of the right side: 3.468274156

Break this problem into two subproblems by setting 
(X + -2.727272728) equal to 3.468274156 and -3.468274156.


Subproblem 1
X + -2.727272728 = 3.468274156

Simplifying
X + -2.727272728 = 3.468274156

Reorder the terms:
-2.727272728 + X = 3.468274156

Solving
-2.727272728 + X = 3.468274156

Solving for variable 'X'.

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

Add '2.727272728' to each side of the equation.
-2.727272728 + 2.727272728 + X = 3.468274156 + 2.727272728

Combine like terms: -2.727272728 + 2.727272728 = 0.000000000
0.000000000 + X = 3.468274156 + 2.727272728
X = 3.468274156 + 2.727272728

Combine like terms: 3.468274156 + 2.727272728 = 6.195546884
X = 6.195546884

Simplifying
X = 6.195546884


Subproblem 2
X + -2.727272728 = -3.468274156

Simplifying
X + -2.727272728 = -3.468274156

Reorder the terms:
-2.727272728 + X = -3.468274156

Solving
-2.727272728 + X = -3.468274156

Solving for variable 'X'.

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

Add '2.727272728' to each side of the equation.
-2.727272728 + 2.727272728 + X = -3.468274156 + 2.727272728

Combine like terms: -2.727272728 + 2.727272728 = 0.000000000
0.000000000 + X = -3.468274156 + 2.727272728
X = -3.468274156 + 2.727272728

Combine like terms: -3.468274156 + 2.727272728 = -0.741001428
X = -0.741001428

Simplifying
X = -0.741001428


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.195546884, -0.741001428}

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