w(w+400)=6000

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Solution for w(w+400)=6000 equation:


Simplifying
w(w + 400) = 6000

Reorder the terms:
w(400 + w) = 6000
(400 * w + w * w) = 6000
(400w + w2) = 6000

Solving
400w + w2 = 6000

Solving for variable 'w'.

Reorder the terms:
-6000 + 400w + w2 = 6000 + -6000

Combine like terms: 6000 + -6000 = 0
-6000 + 400w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6000' to each side of the equation.
-6000 + 400w + 6000 + w2 = 0 + 6000

Reorder the terms:
-6000 + 6000 + 400w + w2 = 0 + 6000

Combine like terms: -6000 + 6000 = 0
0 + 400w + w2 = 0 + 6000
400w + w2 = 0 + 6000

Combine like terms: 0 + 6000 = 6000
400w + w2 = 6000

The w term is 400w.  Take half its coefficient (200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
400w + 40000 + w2 = 6000 + 40000

Reorder the terms:
40000 + 400w + w2 = 6000 + 40000

Combine like terms: 6000 + 40000 = 46000
40000 + 400w + w2 = 46000

Factor a perfect square on the left side:
(w + 200)(w + 200) = 46000

Calculate the square root of the right side: 214.476105895

Break this problem into two subproblems by setting 
(w + 200) equal to 214.476105895 and -214.476105895.

Subproblem 1

w + 200 = 214.476105895 Simplifying w + 200 = 214.476105895 Reorder the terms: 200 + w = 214.476105895 Solving 200 + w = 214.476105895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + w = 214.476105895 + -200 Combine like terms: 200 + -200 = 0 0 + w = 214.476105895 + -200 w = 214.476105895 + -200 Combine like terms: 214.476105895 + -200 = 14.476105895 w = 14.476105895 Simplifying w = 14.476105895

Subproblem 2

w + 200 = -214.476105895 Simplifying w + 200 = -214.476105895 Reorder the terms: 200 + w = -214.476105895 Solving 200 + w = -214.476105895 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-200' to each side of the equation. 200 + -200 + w = -214.476105895 + -200 Combine like terms: 200 + -200 = 0 0 + w = -214.476105895 + -200 w = -214.476105895 + -200 Combine like terms: -214.476105895 + -200 = -414.476105895 w = -414.476105895 Simplifying w = -414.476105895

Solution

The solution to the problem is based on the solutions from the subproblems. w = {14.476105895, -414.476105895}

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