0.16x(x+65)+0.36(x+85)=-37

Solution for 0.16x(x+65)+0.36(x+85)=-37 equation:

Simplifying
0.16x(x + 65) + 0.36(x + 85) = -37

Reorder the terms:
0.16x(65 + x) + 0.36(x + 85) = -37
(65 * 0.16x + x * 0.16x) + 0.36(x + 85) = -37
(10.4x + 0.16x2) + 0.36(x + 85) = -37

Reorder the terms:
10.4x + 0.16x2 + 0.36(85 + x) = -37
10.4x + 0.16x2 + (85 * 0.36 + x * 0.36) = -37
10.4x + 0.16x2 + (30.6 + 0.36x) = -37

Reorder the terms:
30.6 + 10.4x + 0.36x + 0.16x2 = -37

Combine like terms: 10.4x + 0.36x = 10.76x
30.6 + 10.76x + 0.16x2 = -37

Solving
30.6 + 10.76x + 0.16x2 = -37

Solving for variable 'x'.

Reorder the terms:
30.6 + 37 + 10.76x + 0.16x2 = -37 + 37

Combine like terms: 30.6 + 37 = 67.6
67.6 + 10.76x + 0.16x2 = -37 + 37

Combine like terms: -37 + 37 = 0
67.6 + 10.76x + 0.16x2 = 0

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

Divide each side by '0.16'.
422.5 + 67.25x + x2 = 0

Move the constant term to the right:

Add '-422.5' to each side of the equation.
422.5 + 67.25x + -422.5 + x2 = 0 + -422.5

Reorder the terms:
422.5 + -422.5 + 67.25x + x2 = 0 + -422.5

Combine like terms: 422.5 + -422.5 = 0.0
0.0 + 67.25x + x2 = 0 + -422.5
67.25x + x2 = 0 + -422.5

Combine like terms: 0 + -422.5 = -422.5
67.25x + x2 = -422.5

The x term is 67.25x.  Take half its coefficient (33.625).
Square it (1130.640625) and add it to both sides.

Add '1130.640625' to each side of the equation.
67.25x + 1130.640625 + x2 = -422.5 + 1130.640625

Reorder the terms:
1130.640625 + 67.25x + x2 = -422.5 + 1130.640625

Combine like terms: -422.5 + 1130.640625 = 708.140625
1130.640625 + 67.25x + x2 = 708.140625

Factor a perfect square on the left side:
(x + 33.625)(x + 33.625) = 708.140625

Calculate the square root of the right side: 26.610911766

Break this problem into two subproblems by setting 
(x + 33.625) equal to 26.610911766 and -26.610911766.

Subproblem 1
x + 33.625 = 26.610911766

Simplifying
x + 33.625 = 26.610911766

Reorder the terms:
33.625 + x = 26.610911766

Solving
33.625 + x = 26.610911766

Solving for variable 'x'.

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

Add '-33.625' to each side of the equation.
33.625 + -33.625 + x = 26.610911766 + -33.625

Combine like terms: 33.625 + -33.625 = 0.000
0.000 + x = 26.610911766 + -33.625
x = 26.610911766 + -33.625

Combine like terms: 26.610911766 + -33.625 = -7.014088234
x = -7.014088234

Simplifying
x = -7.014088234

Subproblem 2
x + 33.625 = -26.610911766

Simplifying
x + 33.625 = -26.610911766

Reorder the terms:
33.625 + x = -26.610911766

Solving
33.625 + x = -26.610911766

Solving for variable 'x'.

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

Add '-33.625' to each side of the equation.
33.625 + -33.625 + x = -26.610911766 + -33.625

Combine like terms: 33.625 + -33.625 = 0.000
0.000 + x = -26.610911766 + -33.625
x = -26.610911766 + -33.625

Combine like terms: -26.610911766 + -33.625 = -60.235911766
x = -60.235911766

Simplifying
x = -60.235911766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.014088234, -60.235911766}