w(w+400)=60

Solution for w(w+400)=60 equation:

Simplifying
w(w + 400) = 60

Reorder the terms:
w(400 + w) = 60
(400 * w + w * w) = 60
(400w + w2) = 60

Solving
400w + w2 = 60

Solving for variable 'w'.

Reorder the terms:
-60 + 400w + w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 400w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 400w + 60 + w2 = 0 + 60

Reorder the terms:
-60 + 60 + 400w + w2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 400w + w2 = 0 + 60
400w + w2 = 0 + 60

Combine like terms: 0 + 60 = 60
400w + w2 = 60

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 = 60 + 40000

Reorder the terms:
40000 + 400w + w2 = 60 + 40000

Combine like terms: 60 + 40000 = 40060
40000 + 400w + w2 = 40060

Factor a perfect square on the left side:
(w + 200)(w + 200) = 40060

Calculate the square root of the right side: 200.149943792

Break this problem into two subproblems by setting 
(w + 200) equal to 200.149943792 and -200.149943792.

Subproblem 1
w + 200 = 200.149943792

Simplifying
w + 200 = 200.149943792

Reorder the terms:
200 + w = 200.149943792

Solving
200 + w = 200.149943792

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 = 200.149943792 + -200

Combine like terms: 200 + -200 = 0
0 + w = 200.149943792 + -200
w = 200.149943792 + -200

Combine like terms: 200.149943792 + -200 = 0.149943792
w = 0.149943792

Simplifying
w = 0.149943792

Subproblem 2
w + 200 = -200.149943792

Simplifying
w + 200 = -200.149943792

Reorder the terms:
200 + w = -200.149943792

Solving
200 + w = -200.149943792

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 = -200.149943792 + -200

Combine like terms: 200 + -200 = 0
0 + w = -200.149943792 + -200
w = -200.149943792 + -200

Combine like terms: -200.149943792 + -200 = -400.149943792
w = -400.149943792

Simplifying
w = -400.149943792

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.149943792, -400.149943792}