w^2+1200w-32400=0

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Solution for w^2+1200w-32400=0 equation: 


Simplifying
w2 + 1200w + -32400 = 0

Reorder the terms:
-32400 + 1200w + w2 = 0

Solving
-32400 + 1200w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '32400' to each side of the equation.
-32400 + 1200w + 32400 + w2 = 0 + 32400

Reorder the terms:
-32400 + 32400 + 1200w + w2 = 0 + 32400

Combine like terms: -32400 + 32400 = 0
0 + 1200w + w2 = 0 + 32400
1200w + w2 = 0 + 32400

Combine like terms: 0 + 32400 = 32400
1200w + w2 = 32400

The w term is 1200w.  Take half its coefficient (600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
1200w + 360000 + w2 = 32400 + 360000

Reorder the terms:
360000 + 1200w + w2 = 32400 + 360000

Combine like terms: 32400 + 360000 = 392400
360000 + 1200w + w2 = 392400

Factor a perfect square on the left side:
(w + 600)(w + 600) = 392400

Calculate the square root of the right side: 626.418390535

Break this problem into two subproblems by setting 
(w + 600) equal to 626.418390535 and -626.418390535.


Subproblem 1
w + 600 = 626.418390535

Simplifying
w + 600 = 626.418390535

Reorder the terms:
600 + w = 626.418390535

Solving
600 + w = 626.418390535

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-600' to each side of the equation.
600 + -600 + w = 626.418390535 + -600

Combine like terms: 600 + -600 = 0
0 + w = 626.418390535 + -600
w = 626.418390535 + -600

Combine like terms: 626.418390535 + -600 = 26.418390535
w = 26.418390535

Simplifying
w = 26.418390535


Subproblem 2
w + 600 = -626.418390535

Simplifying
w + 600 = -626.418390535

Reorder the terms:
600 + w = -626.418390535

Solving
600 + w = -626.418390535

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-600' to each side of the equation.
600 + -600 + w = -626.418390535 + -600

Combine like terms: 600 + -600 = 0
0 + w = -626.418390535 + -600
w = -626.418390535 + -600

Combine like terms: -626.418390535 + -600 = -1226.418390535
w = -1226.418390535

Simplifying
w = -1226.418390535


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {26.418390535, -1226.418390535}

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