3q^2-12q+5=0

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Solution for 3q^2-12q+5=0 equation: 


Simplifying
3q2 + -12q + 5 = 0

Reorder the terms:
5 + -12q + 3q2 = 0

Solving
5 + -12q + 3q2 = 0

Solving for variable 'q'.

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

Divide each side by '3'.
1.666666667 + -4q + q2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -4q + -1.666666667 + q2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -4q + q2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -4q + q2 = 0 + -1.666666667
-4q + q2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-4q + q2 = -1.666666667

The q term is -4q.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4q + 4 + q2 = -1.666666667 + 4

Reorder the terms:
4 + -4q + q2 = -1.666666667 + 4

Combine like terms: -1.666666667 + 4 = 2.333333333
4 + -4q + q2 = 2.333333333

Factor a perfect square on the left side:
(q + -2)(q + -2) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(q + -2) equal to 1.527525232 and -1.527525232.


Subproblem 1
q + -2 = 1.527525232

Simplifying
q + -2 = 1.527525232

Reorder the terms:
-2 + q = 1.527525232

Solving
-2 + q = 1.527525232

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = 1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + q = 1.527525232 + 2
q = 1.527525232 + 2

Combine like terms: 1.527525232 + 2 = 3.527525232
q = 3.527525232

Simplifying
q = 3.527525232


Subproblem 2
q + -2 = -1.527525232

Simplifying
q + -2 = -1.527525232

Reorder the terms:
-2 + q = -1.527525232

Solving
-2 + q = -1.527525232

Solving for variable 'q'.

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

Add '2' to each side of the equation.
-2 + 2 + q = -1.527525232 + 2

Combine like terms: -2 + 2 = 0
0 + q = -1.527525232 + 2
q = -1.527525232 + 2

Combine like terms: -1.527525232 + 2 = 0.472474768
q = 0.472474768

Simplifying
q = 0.472474768


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.527525232, 0.472474768}

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