(1000-q)q-22500+400=

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Solution for (1000-q)q-22500+400= equation:


Simplifying
(1000 + -1q) * q + -22500 + 400 = 0

Reorder the terms for easier multiplication:
q(1000 + -1q) + -22500 + 400 = 0
(1000 * q + -1q * q) + -22500 + 400 = 0
(1000q + -1q2) + -22500 + 400 = 0

Reorder the terms:
-22500 + 400 + 1000q + -1q2 = 0

Combine like terms: -22500 + 400 = -22100
-22100 + 1000q + -1q2 = 0

Solving
-22100 + 1000q + -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'.
22100 + -1000q + q2 = 0

Move the constant term to the right:

Add '-22100' to each side of the equation.
22100 + -1000q + -22100 + q2 = 0 + -22100

Reorder the terms:
22100 + -22100 + -1000q + q2 = 0 + -22100

Combine like terms: 22100 + -22100 = 0
0 + -1000q + q2 = 0 + -22100
-1000q + q2 = 0 + -22100

Combine like terms: 0 + -22100 = -22100
-1000q + q2 = -22100

The q term is -1000q.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000q + 250000 + q2 = -22100 + 250000

Reorder the terms:
250000 + -1000q + q2 = -22100 + 250000

Combine like terms: -22100 + 250000 = 227900
250000 + -1000q + q2 = 227900

Factor a perfect square on the left side:
(q + -500)(q + -500) = 227900

Calculate the square root of the right side: 477.388730491

Break this problem into two subproblems by setting 
(q + -500) equal to 477.388730491 and -477.388730491.

Subproblem 1

q + -500 = 477.388730491 Simplifying q + -500 = 477.388730491 Reorder the terms: -500 + q = 477.388730491 Solving -500 + q = 477.388730491 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = 477.388730491 + 500 Combine like terms: -500 + 500 = 0 0 + q = 477.388730491 + 500 q = 477.388730491 + 500 Combine like terms: 477.388730491 + 500 = 977.388730491 q = 977.388730491 Simplifying q = 977.388730491

Subproblem 2

q + -500 = -477.388730491 Simplifying q + -500 = -477.388730491 Reorder the terms: -500 + q = -477.388730491 Solving -500 + q = -477.388730491 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = -477.388730491 + 500 Combine like terms: -500 + 500 = 0 0 + q = -477.388730491 + 500 q = -477.388730491 + 500 Combine like terms: -477.388730491 + 500 = 22.611269509 q = 22.611269509 Simplifying q = 22.611269509

Solution

The solution to the problem is based on the solutions from the subproblems. q = {977.388730491, 22.611269509}

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