40000=200w+w^2

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Solution for 40000=200w+w^2 equation:


Simplifying
40000 = 200w + w2

Solving
40000 = 200w + w2

Solving for variable 'w'.

Reorder the terms:
40000 + -200w + -1w2 = 200w + -200w + w2 + -1w2

Combine like terms: 200w + -200w = 0
40000 + -200w + -1w2 = 0 + w2 + -1w2
40000 + -200w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
40000 + -200w + -1w2 = 0

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

Divide each side by '-1'.
-40000 + 200w + w2 = 0

Move the constant term to the right:

Add '40000' to each side of the equation.
-40000 + 200w + 40000 + w2 = 0 + 40000

Reorder the terms:
-40000 + 40000 + 200w + w2 = 0 + 40000

Combine like terms: -40000 + 40000 = 0
0 + 200w + w2 = 0 + 40000
200w + w2 = 0 + 40000

Combine like terms: 0 + 40000 = 40000
200w + w2 = 40000

The w term is 200w.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200w + 10000 + w2 = 40000 + 10000

Reorder the terms:
10000 + 200w + w2 = 40000 + 10000

Combine like terms: 40000 + 10000 = 50000
10000 + 200w + w2 = 50000

Factor a perfect square on the left side:
(w + 100)(w + 100) = 50000

Calculate the square root of the right side: 223.60679775

Break this problem into two subproblems by setting 
(w + 100) equal to 223.60679775 and -223.60679775.

Subproblem 1

w + 100 = 223.60679775 Simplifying w + 100 = 223.60679775 Reorder the terms: 100 + w = 223.60679775 Solving 100 + w = 223.60679775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + w = 223.60679775 + -100 Combine like terms: 100 + -100 = 0 0 + w = 223.60679775 + -100 w = 223.60679775 + -100 Combine like terms: 223.60679775 + -100 = 123.60679775 w = 123.60679775 Simplifying w = 123.60679775

Subproblem 2

w + 100 = -223.60679775 Simplifying w + 100 = -223.60679775 Reorder the terms: 100 + w = -223.60679775 Solving 100 + w = -223.60679775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + w = -223.60679775 + -100 Combine like terms: 100 + -100 = 0 0 + w = -223.60679775 + -100 w = -223.60679775 + -100 Combine like terms: -223.60679775 + -100 = -323.60679775 w = -323.60679775 Simplifying w = -323.60679775

Solution

The solution to the problem is based on the solutions from the subproblems. w = {123.60679775, -323.60679775}

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