x^2+2.2x-39.2=0

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Solution for x^2+2.2x-39.2=0 equation: 


Simplifying
x2 + 2.2x + -39.2 = 0

Reorder the terms:
-39.2 + 2.2x + x2 = 0

Solving
-39.2 + 2.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '39.2' to each side of the equation.
-39.2 + 2.2x + 39.2 + x2 = 0 + 39.2

Reorder the terms:
-39.2 + 39.2 + 2.2x + x2 = 0 + 39.2

Combine like terms: -39.2 + 39.2 = 0.0
0.0 + 2.2x + x2 = 0 + 39.2
2.2x + x2 = 0 + 39.2

Combine like terms: 0 + 39.2 = 39.2
2.2x + x2 = 39.2

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = 39.2 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = 39.2 + 1.21

Combine like terms: 39.2 + 1.21 = 40.41
1.21 + 2.2x + x2 = 40.41

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 40.41

Calculate the square root of the right side: 6.35688603

Break this problem into two subproblems by setting 
(x + 1.1) equal to 6.35688603 and -6.35688603.


Subproblem 1
x + 1.1 = 6.35688603

Simplifying
x + 1.1 = 6.35688603

Reorder the terms:
1.1 + x = 6.35688603

Solving
1.1 + x = 6.35688603

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 6.35688603 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 6.35688603 + -1.1
x = 6.35688603 + -1.1

Combine like terms: 6.35688603 + -1.1 = 5.25688603
x = 5.25688603

Simplifying
x = 5.25688603


Subproblem 2
x + 1.1 = -6.35688603

Simplifying
x + 1.1 = -6.35688603

Reorder the terms:
1.1 + x = -6.35688603

Solving
1.1 + x = -6.35688603

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -6.35688603 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -6.35688603 + -1.1
x = -6.35688603 + -1.1

Combine like terms: -6.35688603 + -1.1 = -7.45688603
x = -7.45688603

Simplifying
x = -7.45688603


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.25688603, -7.45688603}

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