x^2+4.2x+3.7=0

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Solution for x^2+4.2x+3.7=0 equation: 


Simplifying
x2 + 4.2x + 3.7 = 0

Reorder the terms:
3.7 + 4.2x + x2 = 0

Solving
3.7 + 4.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3.7' to each side of the equation.
3.7 + 4.2x + -3.7 + x2 = 0 + -3.7

Reorder the terms:
3.7 + -3.7 + 4.2x + x2 = 0 + -3.7

Combine like terms: 3.7 + -3.7 = 0.0
0.0 + 4.2x + x2 = 0 + -3.7
4.2x + x2 = 0 + -3.7

Combine like terms: 0 + -3.7 = -3.7
4.2x + x2 = -3.7

The x term is 4.2x.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2x + 4.41 + x2 = -3.7 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = -3.7 + 4.41

Combine like terms: -3.7 + 4.41 = 0.71
4.41 + 4.2x + x2 = 0.71

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 0.71

Calculate the square root of the right side: 0.842614977

Break this problem into two subproblems by setting 
(x + 2.1) equal to 0.842614977 and -0.842614977.


Subproblem 1
x + 2.1 = 0.842614977

Simplifying
x + 2.1 = 0.842614977

Reorder the terms:
2.1 + x = 0.842614977

Solving
2.1 + x = 0.842614977

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = 0.842614977 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 0.842614977 + -2.1
x = 0.842614977 + -2.1

Combine like terms: 0.842614977 + -2.1 = -1.257385023
x = -1.257385023

Simplifying
x = -1.257385023


Subproblem 2
x + 2.1 = -0.842614977

Simplifying
x + 2.1 = -0.842614977

Reorder the terms:
2.1 + x = -0.842614977

Solving
2.1 + x = -0.842614977

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = -0.842614977 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -0.842614977 + -2.1
x = -0.842614977 + -2.1

Combine like terms: -0.842614977 + -2.1 = -2.942614977
x = -2.942614977

Simplifying
x = -2.942614977


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.257385023, -2.942614977}

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