-2.5x^2-7.1x+2.2=3.7

Solution for -2.5x^2-7.1x+2.2=3.7 equation:

Simplifying
-2.5x2 + -7.1x + 2.2 = 3.7

Reorder the terms:
2.2 + -7.1x + -2.5x2 = 3.7

Solving
2.2 + -7.1x + -2.5x2 = 3.7

Solving for variable 'x'.

Reorder the terms:
2.2 + -3.7 + -7.1x + -2.5x2 = 3.7 + -3.7

Combine like terms: 2.2 + -3.7 = -1.5
-1.5 + -7.1x + -2.5x2 = 3.7 + -3.7

Combine like terms: 3.7 + -3.7 = 0.0
-1.5 + -7.1x + -2.5x2 = 0.0

Begin completing the square.  Divide all terms by
-2.5 the coefficient of the squared term: 

Divide each side by '-2.5'.
0.6 + 2.84x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2.84x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2.84x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2.84x + x2 = 0 + -0.6
2.84x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
2.84x + x2 = -0.6

The x term is 2.84x.  Take half its coefficient (1.42).
Square it (2.0164) and add it to both sides.

Add '2.0164' to each side of the equation.
2.84x + 2.0164 + x2 = -0.6 + 2.0164

Reorder the terms:
2.0164 + 2.84x + x2 = -0.6 + 2.0164

Combine like terms: -0.6 + 2.0164 = 1.4164
2.0164 + 2.84x + x2 = 1.4164

Factor a perfect square on the left side:
(x + 1.42)(x + 1.42) = 1.4164

Calculate the square root of the right side: 1.190126044

Break this problem into two subproblems by setting 
(x + 1.42) equal to 1.190126044 and -1.190126044.

Subproblem 1
x + 1.42 = 1.190126044

Simplifying
x + 1.42 = 1.190126044

Reorder the terms:
1.42 + x = 1.190126044

Solving
1.42 + x = 1.190126044

Solving for variable 'x'.

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

Add '-1.42' to each side of the equation.
1.42 + -1.42 + x = 1.190126044 + -1.42

Combine like terms: 1.42 + -1.42 = 0.00
0.00 + x = 1.190126044 + -1.42
x = 1.190126044 + -1.42

Combine like terms: 1.190126044 + -1.42 = -0.229873956
x = -0.229873956

Simplifying
x = -0.229873956

Subproblem 2
x + 1.42 = -1.190126044

Simplifying
x + 1.42 = -1.190126044

Reorder the terms:
1.42 + x = -1.190126044

Solving
1.42 + x = -1.190126044

Solving for variable 'x'.

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

Add '-1.42' to each side of the equation.
1.42 + -1.42 + x = -1.190126044 + -1.42

Combine like terms: 1.42 + -1.42 = 0.00
0.00 + x = -1.190126044 + -1.42
x = -1.190126044 + -1.42

Combine like terms: -1.190126044 + -1.42 = -2.610126044
x = -2.610126044

Simplifying
x = -2.610126044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.229873956, -2.610126044}