0=-100+(.7q-6)q

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Solution for 0=-100+(.7q-6)q equation:


Simplifying
0 = -100 + (0.7q + -6) * q

Reorder the terms:
0 = -100 + (-6 + 0.7q) * q

Reorder the terms for easier multiplication:
0 = -100 + q(-6 + 0.7q)
0 = -100 + (-6 * q + 0.7q * q)
0 = -100 + (-6q + 0.7q2)

Solving
0 = -100 + -6q + 0.7q2

Solving for variable 'q'.

Combine like terms: 0 + 100 = 100
100 + 6q + -0.7q2 = -100 + -6q + 0.7q2 + 100 + 6q + -0.7q2

Reorder the terms:
100 + 6q + -0.7q2 = -100 + 100 + -6q + 6q + 0.7q2 + -0.7q2

Combine like terms: -100 + 100 = 0
100 + 6q + -0.7q2 = 0 + -6q + 6q + 0.7q2 + -0.7q2
100 + 6q + -0.7q2 = -6q + 6q + 0.7q2 + -0.7q2

Combine like terms: -6q + 6q = 0
100 + 6q + -0.7q2 = 0 + 0.7q2 + -0.7q2
100 + 6q + -0.7q2 = 0.7q2 + -0.7q2

Combine like terms: 0.7q2 + -0.7q2 = 0.0
100 + 6q + -0.7q2 = 0.0

Begin completing the square.  Divide all terms by
-0.7 the coefficient of the squared term: 

Divide each side by '-0.7'.
-142.8571429 + -8.571428571q + q2 = 0

Move the constant term to the right:

Add '142.8571429' to each side of the equation.
-142.8571429 + -8.571428571q + 142.8571429 + q2 = 0 + 142.8571429

Reorder the terms:
-142.8571429 + 142.8571429 + -8.571428571q + q2 = 0 + 142.8571429

Combine like terms: -142.8571429 + 142.8571429 = 0.0000000
0.0000000 + -8.571428571q + q2 = 0 + 142.8571429
-8.571428571q + q2 = 0 + 142.8571429

Combine like terms: 0 + 142.8571429 = 142.8571429
-8.571428571q + q2 = 142.8571429

The q term is -8.571428571q.  Take half its coefficient (-4.285714286).
Square it (18.36734694) and add it to both sides.

Add '18.36734694' to each side of the equation.
-8.571428571q + 18.36734694 + q2 = 142.8571429 + 18.36734694

Reorder the terms:
18.36734694 + -8.571428571q + q2 = 142.8571429 + 18.36734694

Combine like terms: 142.8571429 + 18.36734694 = 161.22448984
18.36734694 + -8.571428571q + q2 = 161.22448984

Factor a perfect square on the left side:
(q + -4.285714286)(q + -4.285714286) = 161.22448984

Calculate the square root of the right side: 12.697420598

Break this problem into two subproblems by setting 
(q + -4.285714286) equal to 12.697420598 and -12.697420598.

Subproblem 1

q + -4.285714286 = 12.697420598 Simplifying q + -4.285714286 = 12.697420598 Reorder the terms: -4.285714286 + q = 12.697420598 Solving -4.285714286 + q = 12.697420598 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + q = 12.697420598 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + q = 12.697420598 + 4.285714286 q = 12.697420598 + 4.285714286 Combine like terms: 12.697420598 + 4.285714286 = 16.983134884 q = 16.983134884 Simplifying q = 16.983134884

Subproblem 2

q + -4.285714286 = -12.697420598 Simplifying q + -4.285714286 = -12.697420598 Reorder the terms: -4.285714286 + q = -12.697420598 Solving -4.285714286 + q = -12.697420598 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.285714286' to each side of the equation. -4.285714286 + 4.285714286 + q = -12.697420598 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + q = -12.697420598 + 4.285714286 q = -12.697420598 + 4.285714286 Combine like terms: -12.697420598 + 4.285714286 = -8.411706312 q = -8.411706312 Simplifying q = -8.411706312

Solution

The solution to the problem is based on the solutions from the subproblems. q = {16.983134884, -8.411706312}

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