-0.6x-0.05x^2+32=0

Solution for -0.6x-0.05x^2+32=0 equation:

Simplifying
-0.6x + -0.05x2 + 32 = 0

Reorder the terms:
32 + -0.6x + -0.05x2 = 0

Solving
32 + -0.6x + -0.05x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
-640 + 12x + x2 = 0

Move the constant term to the right:

Add '640' to each side of the equation.
-640 + 12x + 640 + x2 = 0 + 640

Reorder the terms:
-640 + 640 + 12x + x2 = 0 + 640

Combine like terms: -640 + 640 = 0
0 + 12x + x2 = 0 + 640
12x + x2 = 0 + 640

Combine like terms: 0 + 640 = 640
12x + x2 = 640

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 640 + 36

Reorder the terms:
36 + 12x + x2 = 640 + 36

Combine like terms: 640 + 36 = 676
36 + 12x + x2 = 676

Factor a perfect square on the left side:
(x + 6)(x + 6) = 676

Calculate the square root of the right side: 26

Break this problem into two subproblems by setting 
(x + 6) equal to 26 and -26.

Subproblem 1
x + 6 = 26

Simplifying
x + 6 = 26

Reorder the terms:
6 + x = 26

Solving
6 + x = 26

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 26 + -6

Combine like terms: 6 + -6 = 0
0 + x = 26 + -6
x = 26 + -6

Combine like terms: 26 + -6 = 20
x = 20

Simplifying
x = 20

Subproblem 2
x + 6 = -26

Simplifying
x + 6 = -26

Reorder the terms:
6 + x = -26

Solving
6 + x = -26

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -26 + -6

Combine like terms: 6 + -6 = 0
0 + x = -26 + -6
x = -26 + -6

Combine like terms: -26 + -6 = -32
x = -32

Simplifying
x = -32

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20, -32}