0.04+0.4q+q^2=1

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Solution for 0.04+0.4q+q^2=1 equation: 


Simplifying
0.04 + 0.4q + q2 = 1

Solving
0.04 + 0.4q + q2 = 1

Solving for variable 'q'.

Reorder the terms:
0.04 + -1 + 0.4q + q2 = 1 + -1

Combine like terms: 0.04 + -1 = -0.96
-0.96 + 0.4q + q2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.96 + 0.4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.96' to each side of the equation.
-0.96 + 0.4q + 0.96 + q2 = 0 + 0.96

Reorder the terms:
-0.96 + 0.96 + 0.4q + q2 = 0 + 0.96

Combine like terms: -0.96 + 0.96 = 0.00
0.00 + 0.4q + q2 = 0 + 0.96
0.4q + q2 = 0 + 0.96

Combine like terms: 0 + 0.96 = 0.96
0.4q + q2 = 0.96

The q term is 0.4q.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4q + 0.04 + q2 = 0.96 + 0.04

Reorder the terms:
0.04 + 0.4q + q2 = 0.96 + 0.04

Combine like terms: 0.96 + 0.04 = 1
0.04 + 0.4q + q2 = 1

Factor a perfect square on the left side:
(q + 0.2)(q + 0.2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(q + 0.2) equal to 1 and -1.


Subproblem 1
q + 0.2 = 1

Simplifying
q + 0.2 = 1

Reorder the terms:
0.2 + q = 1

Solving
0.2 + q = 1

Solving for variable 'q'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + q = 1 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + q = 1 + -0.2
q = 1 + -0.2

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

Simplifying
q = 0.8


Subproblem 2
q + 0.2 = -1

Simplifying
q + 0.2 = -1

Reorder the terms:
0.2 + q = -1

Solving
0.2 + q = -1

Solving for variable 'q'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + q = -1 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + q = -1 + -0.2
q = -1 + -0.2

Combine like terms: -1 + -0.2 = -1.2
q = -1.2

Simplifying
q = -1.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.8, -1.2}

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