.2x^2+3.7x-1.9=0

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Solution for .2x^2+3.7x-1.9=0 equation: 


Simplifying
0.2x2 + 3.7x + -1.9 = 0

Reorder the terms:
-1.9 + 3.7x + 0.2x2 = 0

Solving
-1.9 + 3.7x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
-9.5 + 18.5x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + 18.5x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + 18.5x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + 18.5x + x2 = 0 + 9.5
18.5x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
18.5x + x2 = 9.5

The x term is 18.5x.  Take half its coefficient (9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
18.5x + 85.5625 + x2 = 9.5 + 85.5625

Reorder the terms:
85.5625 + 18.5x + x2 = 9.5 + 85.5625

Combine like terms: 9.5 + 85.5625 = 95.0625
85.5625 + 18.5x + x2 = 95.0625

Factor a perfect square on the left side:
(x + 9.25)(x + 9.25) = 95.0625

Calculate the square root of the right side: 9.75

Break this problem into two subproblems by setting 
(x + 9.25) equal to 9.75 and -9.75.


Subproblem 1
x + 9.25 = 9.75

Simplifying
x + 9.25 = 9.75

Reorder the terms:
9.25 + x = 9.75

Solving
9.25 + x = 9.75

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = 9.75 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = 9.75 + -9.25
x = 9.75 + -9.25

Combine like terms: 9.75 + -9.25 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 9.25 = -9.75

Simplifying
x + 9.25 = -9.75

Reorder the terms:
9.25 + x = -9.75

Solving
9.25 + x = -9.75

Solving for variable 'x'.

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

Add '-9.25' to each side of the equation.
9.25 + -9.25 + x = -9.75 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + x = -9.75 + -9.25
x = -9.75 + -9.25

Combine like terms: -9.75 + -9.25 = -19
x = -19

Simplifying
x = -19


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -19}

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