12+q(5-q)=0

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Solution for 12+q(5-q)=0 equation:


Simplifying
12 + q(5 + -1q) = 0
12 + (5 * q + -1q * q) = 0
12 + (5q + -1q2) = 0

Solving
12 + 5q + -1q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -5q + q2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -5q + 12 + q2 = 0 + 12

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

Combine like terms: -12 + 12 = 0
0 + -5q + q2 = 0 + 12
-5q + q2 = 0 + 12

Combine like terms: 0 + 12 = 12
-5q + q2 = 12

The q term is -5q.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5q + 6.25 + q2 = 12 + 6.25

Reorder the terms:
6.25 + -5q + q2 = 12 + 6.25

Combine like terms: 12 + 6.25 = 18.25
6.25 + -5q + q2 = 18.25

Factor a perfect square on the left side:
(q + -2.5)(q + -2.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(q + -2.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

q + -2.5 = 4.272001873 Simplifying q + -2.5 = 4.272001873 Reorder the terms: -2.5 + q = 4.272001873 Solving -2.5 + q = 4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = 4.272001873 + 2.5 q = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 q = 6.772001873 Simplifying q = 6.772001873

Subproblem 2

q + -2.5 = -4.272001873 Simplifying q + -2.5 = -4.272001873 Reorder the terms: -2.5 + q = -4.272001873 Solving -2.5 + q = -4.272001873 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + q = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + q = -4.272001873 + 2.5 q = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 q = -1.772001873 Simplifying q = -1.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. q = {6.772001873, -1.772001873}

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