1.1x^2+7.3x-13.8=0

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Solution for 1.1x^2+7.3x-13.8=0 equation: 


Simplifying
1.1x2 + 7.3x + -13.8 = 0

Reorder the terms:
-13.8 + 7.3x + 1.1x2 = 0

Solving
-13.8 + 7.3x + 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'.
-12.54545455 + 6.636363636x + x2 = 0

Move the constant term to the right:

Add '12.54545455' to each side of the equation.
-12.54545455 + 6.636363636x + 12.54545455 + x2 = 0 + 12.54545455

Reorder the terms:
-12.54545455 + 12.54545455 + 6.636363636x + x2 = 0 + 12.54545455

Combine like terms: -12.54545455 + 12.54545455 = 0.00000000
0.00000000 + 6.636363636x + x2 = 0 + 12.54545455
6.636363636x + x2 = 0 + 12.54545455

Combine like terms: 0 + 12.54545455 = 12.54545455
6.636363636x + x2 = 12.54545455

The x term is 6.636363636x.  Take half its coefficient (3.318181818).
Square it (11.01033058) and add it to both sides.

Add '11.01033058' to each side of the equation.
6.636363636x + 11.01033058 + x2 = 12.54545455 + 11.01033058

Reorder the terms:
11.01033058 + 6.636363636x + x2 = 12.54545455 + 11.01033058

Combine like terms: 12.54545455 + 11.01033058 = 23.55578513
11.01033058 + 6.636363636x + x2 = 23.55578513

Factor a perfect square on the left side:
(x + 3.318181818)(x + 3.318181818) = 23.55578513

Calculate the square root of the right side: 4.853430244

Break this problem into two subproblems by setting 
(x + 3.318181818) equal to 4.853430244 and -4.853430244.


Subproblem 1
x + 3.318181818 = 4.853430244

Simplifying
x + 3.318181818 = 4.853430244

Reorder the terms:
3.318181818 + x = 4.853430244

Solving
3.318181818 + x = 4.853430244

Solving for variable 'x'.

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

Add '-3.318181818' to each side of the equation.
3.318181818 + -3.318181818 + x = 4.853430244 + -3.318181818

Combine like terms: 3.318181818 + -3.318181818 = 0.000000000
0.000000000 + x = 4.853430244 + -3.318181818
x = 4.853430244 + -3.318181818

Combine like terms: 4.853430244 + -3.318181818 = 1.535248426
x = 1.535248426

Simplifying
x = 1.535248426


Subproblem 2
x + 3.318181818 = -4.853430244

Simplifying
x + 3.318181818 = -4.853430244

Reorder the terms:
3.318181818 + x = -4.853430244

Solving
3.318181818 + x = -4.853430244

Solving for variable 'x'.

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

Add '-3.318181818' to each side of the equation.
3.318181818 + -3.318181818 + x = -4.853430244 + -3.318181818

Combine like terms: 3.318181818 + -3.318181818 = 0.000000000
0.000000000 + x = -4.853430244 + -3.318181818
x = -4.853430244 + -3.318181818

Combine like terms: -4.853430244 + -3.318181818 = -8.171612062
x = -8.171612062

Simplifying
x = -8.171612062


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.535248426, -8.171612062}

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