x^2+5.2x+2.1=0

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Solution for x^2+5.2x+2.1=0 equation: 


Simplifying
x2 + 5.2x + 2.1 = 0

Reorder the terms:
2.1 + 5.2x + x2 = 0

Solving
2.1 + 5.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + 5.2x + -2.1 + x2 = 0 + -2.1

Reorder the terms:
2.1 + -2.1 + 5.2x + x2 = 0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + 5.2x + x2 = 0 + -2.1
5.2x + x2 = 0 + -2.1

Combine like terms: 0 + -2.1 = -2.1
5.2x + x2 = -2.1

The x term is 5.2x.  Take half its coefficient (2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
5.2x + 6.76 + x2 = -2.1 + 6.76

Reorder the terms:
6.76 + 5.2x + x2 = -2.1 + 6.76

Combine like terms: -2.1 + 6.76 = 4.66
6.76 + 5.2x + x2 = 4.66

Factor a perfect square on the left side:
(x + 2.6)(x + 2.6) = 4.66

Calculate the square root of the right side: 2.158703314

Break this problem into two subproblems by setting 
(x + 2.6) equal to 2.158703314 and -2.158703314.


Subproblem 1
x + 2.6 = 2.158703314

Simplifying
x + 2.6 = 2.158703314

Reorder the terms:
2.6 + x = 2.158703314

Solving
2.6 + x = 2.158703314

Solving for variable 'x'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + x = 2.158703314 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + x = 2.158703314 + -2.6
x = 2.158703314 + -2.6

Combine like terms: 2.158703314 + -2.6 = -0.441296686
x = -0.441296686

Simplifying
x = -0.441296686


Subproblem 2
x + 2.6 = -2.158703314

Simplifying
x + 2.6 = -2.158703314

Reorder the terms:
2.6 + x = -2.158703314

Solving
2.6 + x = -2.158703314

Solving for variable 'x'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + x = -2.158703314 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + x = -2.158703314 + -2.6
x = -2.158703314 + -2.6

Combine like terms: -2.158703314 + -2.6 = -4.758703314
x = -4.758703314

Simplifying
x = -4.758703314


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.441296686, -4.758703314}

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