q^2-0.02618-0.9548q=0

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Solution for q^2-0.02618-0.9548q=0 equation: 


Simplifying
q2 + -0.02618 + -0.9548q = 0

Reorder the terms:
-0.02618 + -0.9548q + q2 = 0

Solving
-0.02618 + -0.9548q + q2 = 0

Solving for variable 'q'.

Begin completing the square.

Move the constant term to the right:

Add '0.02618' to each side of the equation.
-0.02618 + -0.9548q + 0.02618 + q2 = 0 + 0.02618

Reorder the terms:
-0.02618 + 0.02618 + -0.9548q + q2 = 0 + 0.02618

Combine like terms: -0.02618 + 0.02618 = 0.00000
0.00000 + -0.9548q + q2 = 0 + 0.02618
-0.9548q + q2 = 0 + 0.02618

Combine like terms: 0 + 0.02618 = 0.02618
-0.9548q + q2 = 0.02618

The q term is -0.9548q.  Take half its coefficient (-0.4774).
Square it (0.22791076) and add it to both sides.

Add '0.22791076' to each side of the equation.
-0.9548q + 0.22791076 + q2 = 0.02618 + 0.22791076

Reorder the terms:
0.22791076 + -0.9548q + q2 = 0.02618 + 0.22791076

Combine like terms: 0.02618 + 0.22791076 = 0.25409076
0.22791076 + -0.9548q + q2 = 0.25409076

Factor a perfect square on the left side:
(q + -0.4774)(q + -0.4774) = 0.25409076

Calculate the square root of the right side: 0.504074161

Break this problem into two subproblems by setting 
(q + -0.4774) equal to 0.504074161 and -0.504074161.


Subproblem 1
q + -0.4774 = 0.504074161

Simplifying
q + -0.4774 = 0.504074161

Reorder the terms:
-0.4774 + q = 0.504074161

Solving
-0.4774 + q = 0.504074161

Solving for variable 'q'.

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

Add '0.4774' to each side of the equation.
-0.4774 + 0.4774 + q = 0.504074161 + 0.4774

Combine like terms: -0.4774 + 0.4774 = 0.0000
0.0000 + q = 0.504074161 + 0.4774
q = 0.504074161 + 0.4774

Combine like terms: 0.504074161 + 0.4774 = 0.981474161
q = 0.981474161

Simplifying
q = 0.981474161


Subproblem 2
q + -0.4774 = -0.504074161

Simplifying
q + -0.4774 = -0.504074161

Reorder the terms:
-0.4774 + q = -0.504074161

Solving
-0.4774 + q = -0.504074161

Solving for variable 'q'.

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

Add '0.4774' to each side of the equation.
-0.4774 + 0.4774 + q = -0.504074161 + 0.4774

Combine like terms: -0.4774 + 0.4774 = 0.0000
0.0000 + q = -0.504074161 + 0.4774
q = -0.504074161 + 0.4774

Combine like terms: -0.504074161 + 0.4774 = -0.026674161
q = -0.026674161

Simplifying
q = -0.026674161


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.981474161, -0.026674161}

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