1.1x^2-6.3x+4.2=0

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Solution for 1.1x^2-6.3x+4.2=0 equation: 


Simplifying
1.1x2 + -6.3x + 4.2 = 0

Reorder the terms:
4.2 + -6.3x + 1.1x2 = 0

Solving
4.2 + -6.3x + 1.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.1'.
3.818181818 + -5.727272727x + x2 = 0

Move the constant term to the right:

Add '-3.818181818' to each side of the equation.
3.818181818 + -5.727272727x + -3.818181818 + x2 = 0 + -3.818181818

Reorder the terms:
3.818181818 + -3.818181818 + -5.727272727x + x2 = 0 + -3.818181818

Combine like terms: 3.818181818 + -3.818181818 = 0.000000000
0.000000000 + -5.727272727x + x2 = 0 + -3.818181818
-5.727272727x + x2 = 0 + -3.818181818

Combine like terms: 0 + -3.818181818 = -3.818181818
-5.727272727x + x2 = -3.818181818

The x term is -5.727272727x.  Take half its coefficient (-2.863636364).
Square it (8.200413225) and add it to both sides.

Add '8.200413225' to each side of the equation.
-5.727272727x + 8.200413225 + x2 = -3.818181818 + 8.200413225

Reorder the terms:
8.200413225 + -5.727272727x + x2 = -3.818181818 + 8.200413225

Combine like terms: -3.818181818 + 8.200413225 = 4.382231407
8.200413225 + -5.727272727x + x2 = 4.382231407

Factor a perfect square on the left side:
(x + -2.863636364)(x + -2.863636364) = 4.382231407

Calculate the square root of the right side: 2.09337799

Break this problem into two subproblems by setting 
(x + -2.863636364) equal to 2.09337799 and -2.09337799.


Subproblem 1
x + -2.863636364 = 2.09337799

Simplifying
x + -2.863636364 = 2.09337799

Reorder the terms:
-2.863636364 + x = 2.09337799

Solving
-2.863636364 + x = 2.09337799

Solving for variable 'x'.

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

Add '2.863636364' to each side of the equation.
-2.863636364 + 2.863636364 + x = 2.09337799 + 2.863636364

Combine like terms: -2.863636364 + 2.863636364 = 0.000000000
0.000000000 + x = 2.09337799 + 2.863636364
x = 2.09337799 + 2.863636364

Combine like terms: 2.09337799 + 2.863636364 = 4.957014354
x = 4.957014354

Simplifying
x = 4.957014354


Subproblem 2
x + -2.863636364 = -2.09337799

Simplifying
x + -2.863636364 = -2.09337799

Reorder the terms:
-2.863636364 + x = -2.09337799

Solving
-2.863636364 + x = -2.09337799

Solving for variable 'x'.

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

Add '2.863636364' to each side of the equation.
-2.863636364 + 2.863636364 + x = -2.09337799 + 2.863636364

Combine like terms: -2.863636364 + 2.863636364 = 0.000000000
0.000000000 + x = -2.09337799 + 2.863636364
x = -2.09337799 + 2.863636364

Combine like terms: -2.09337799 + 2.863636364 = 0.770258374
x = 0.770258374

Simplifying
x = 0.770258374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.957014354, 0.770258374}

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