q^2+1.6q-.36=0

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Solution for q^2+1.6q-.36=0 equation: 


Simplifying
q2 + 1.6q + -0.36 = 0

Reorder the terms:
-0.36 + 1.6q + q2 = 0

Solving
-0.36 + 1.6q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '0.36' to each side of the equation.
-0.36 + 1.6q + 0.36 + q2 = 0 + 0.36

Reorder the terms:
-0.36 + 0.36 + 1.6q + q2 = 0 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.00 + 1.6q + q2 = 0 + 0.36
1.6q + q2 = 0 + 0.36

Combine like terms: 0 + 0.36 = 0.36
1.6q + q2 = 0.36

The q term is 1.6q.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6q + 0.64 + q2 = 0.36 + 0.64

Reorder the terms:
0.64 + 1.6q + q2 = 0.36 + 0.64

Combine like terms: 0.36 + 0.64 = 1
0.64 + 1.6q + q2 = 1

Factor a perfect square on the left side:
(q + 0.8)(q + 0.8) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(q + 0.8) equal to 1 and -1.


Subproblem 1
q + 0.8 = 1

Simplifying
q + 0.8 = 1

Reorder the terms:
0.8 + q = 1

Solving
0.8 + q = 1

Solving for variable 'q'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + q = 1 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + q = 1 + -0.8
q = 1 + -0.8

Combine like terms: 1 + -0.8 = 0.2
q = 0.2

Simplifying
q = 0.2


Subproblem 2
q + 0.8 = -1

Simplifying
q + 0.8 = -1

Reorder the terms:
0.8 + q = -1

Solving
0.8 + q = -1

Solving for variable 'q'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + q = -1 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + q = -1 + -0.8
q = -1 + -0.8

Combine like terms: -1 + -0.8 = -1.8
q = -1.8

Simplifying
q = -1.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.2, -1.8}

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