2(6-q)q=1

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Solution for 2(6-q)q=1 equation:


Simplifying
2(6 + -1q) * q = 1

Reorder the terms for easier multiplication:
2q(6 + -1q) = 1
(6 * 2q + -1q * 2q) = 1
(12q + -2q2) = 1

Solving
12q + -2q2 = 1

Solving for variable 'q'.

Reorder the terms:
-1 + 12q + -2q2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 12q + -2q2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -6q + q2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -6q + -0.5 + q2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -6q + q2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -6q + q2 = 0 + -0.5
-6q + q2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-6q + q2 = -0.5

The q term is -6q.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6q + 9 + q2 = -0.5 + 9

Reorder the terms:
9 + -6q + q2 = -0.5 + 9

Combine like terms: -0.5 + 9 = 8.5
9 + -6q + q2 = 8.5

Factor a perfect square on the left side:
(q + -3)(q + -3) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(q + -3) equal to 2.915475947 and -2.915475947.

Subproblem 1

q + -3 = 2.915475947 Simplifying q + -3 = 2.915475947 Reorder the terms: -3 + q = 2.915475947 Solving -3 + q = 2.915475947 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + q = 2.915475947 + 3 Combine like terms: -3 + 3 = 0 0 + q = 2.915475947 + 3 q = 2.915475947 + 3 Combine like terms: 2.915475947 + 3 = 5.915475947 q = 5.915475947 Simplifying q = 5.915475947

Subproblem 2

q + -3 = -2.915475947 Simplifying q + -3 = -2.915475947 Reorder the terms: -3 + q = -2.915475947 Solving -3 + q = -2.915475947 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + q = -2.915475947 + 3 Combine like terms: -3 + 3 = 0 0 + q = -2.915475947 + 3 q = -2.915475947 + 3 Combine like terms: -2.915475947 + 3 = 0.084524053 q = 0.084524053 Simplifying q = 0.084524053

Solution

The solution to the problem is based on the solutions from the subproblems. q = {5.915475947, 0.084524053}

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