5.5x^2+38x-38=0

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Solution for 5.5x^2+38x-38=0 equation: 


Simplifying
5.5x2 + 38x + -38 = 0

Reorder the terms:
-38 + 38x + 5.5x2 = 0

Solving
-38 + 38x + 5.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5.5'.
-6.909090909 + 6.909090909x + x2 = 0

Move the constant term to the right:

Add '6.909090909' to each side of the equation.
-6.909090909 + 6.909090909x + 6.909090909 + x2 = 0 + 6.909090909

Reorder the terms:
-6.909090909 + 6.909090909 + 6.909090909x + x2 = 0 + 6.909090909

Combine like terms: -6.909090909 + 6.909090909 = 0.000000000
0.000000000 + 6.909090909x + x2 = 0 + 6.909090909
6.909090909x + x2 = 0 + 6.909090909

Combine like terms: 0 + 6.909090909 = 6.909090909
6.909090909x + x2 = 6.909090909

The x term is 6.909090909x.  Take half its coefficient (3.454545455).
Square it (11.93388430) and add it to both sides.

Add '11.93388430' to each side of the equation.
6.909090909x + 11.93388430 + x2 = 6.909090909 + 11.93388430

Reorder the terms:
11.93388430 + 6.909090909x + x2 = 6.909090909 + 11.93388430

Combine like terms: 6.909090909 + 11.93388430 = 18.842975209
11.93388430 + 6.909090909x + x2 = 18.842975209

Factor a perfect square on the left side:
(x + 3.454545455)(x + 3.454545455) = 18.842975209

Calculate the square root of the right side: 4.340849595

Break this problem into two subproblems by setting 
(x + 3.454545455) equal to 4.340849595 and -4.340849595.


Subproblem 1
x + 3.454545455 = 4.340849595

Simplifying
x + 3.454545455 = 4.340849595

Reorder the terms:
3.454545455 + x = 4.340849595

Solving
3.454545455 + x = 4.340849595

Solving for variable 'x'.

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

Add '-3.454545455' to each side of the equation.
3.454545455 + -3.454545455 + x = 4.340849595 + -3.454545455

Combine like terms: 3.454545455 + -3.454545455 = 0.000000000
0.000000000 + x = 4.340849595 + -3.454545455
x = 4.340849595 + -3.454545455

Combine like terms: 4.340849595 + -3.454545455 = 0.88630414
x = 0.88630414

Simplifying
x = 0.88630414


Subproblem 2
x + 3.454545455 = -4.340849595

Simplifying
x + 3.454545455 = -4.340849595

Reorder the terms:
3.454545455 + x = -4.340849595

Solving
3.454545455 + x = -4.340849595

Solving for variable 'x'.

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

Add '-3.454545455' to each side of the equation.
3.454545455 + -3.454545455 + x = -4.340849595 + -3.454545455

Combine like terms: 3.454545455 + -3.454545455 = 0.000000000
0.000000000 + x = -4.340849595 + -3.454545455
x = -4.340849595 + -3.454545455

Combine like terms: -4.340849595 + -3.454545455 = -7.79539505
x = -7.79539505

Simplifying
x = -7.79539505


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.88630414, -7.79539505}

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