w^2+30w-600=0

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Solution for w^2+30w-600=0 equation: 


Simplifying
w2 + 30w + -600 = 0

Reorder the terms:
-600 + 30w + w2 = 0

Solving
-600 + 30w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '600' to each side of the equation.
-600 + 30w + 600 + w2 = 0 + 600

Reorder the terms:
-600 + 600 + 30w + w2 = 0 + 600

Combine like terms: -600 + 600 = 0
0 + 30w + w2 = 0 + 600
30w + w2 = 0 + 600

Combine like terms: 0 + 600 = 600
30w + w2 = 600

The w term is 30w.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30w + 225 + w2 = 600 + 225

Reorder the terms:
225 + 30w + w2 = 600 + 225

Combine like terms: 600 + 225 = 825
225 + 30w + w2 = 825

Factor a perfect square on the left side:
(w + 15)(w + 15) = 825

Calculate the square root of the right side: 28.722813233

Break this problem into two subproblems by setting 
(w + 15) equal to 28.722813233 and -28.722813233.


Subproblem 1
w + 15 = 28.722813233

Simplifying
w + 15 = 28.722813233

Reorder the terms:
15 + w = 28.722813233

Solving
15 + w = 28.722813233

Solving for variable 'w'.

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

Add '-15' to each side of the equation.
15 + -15 + w = 28.722813233 + -15

Combine like terms: 15 + -15 = 0
0 + w = 28.722813233 + -15
w = 28.722813233 + -15

Combine like terms: 28.722813233 + -15 = 13.722813233
w = 13.722813233

Simplifying
w = 13.722813233


Subproblem 2
w + 15 = -28.722813233

Simplifying
w + 15 = -28.722813233

Reorder the terms:
15 + w = -28.722813233

Solving
15 + w = -28.722813233

Solving for variable 'w'.

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

Add '-15' to each side of the equation.
15 + -15 + w = -28.722813233 + -15

Combine like terms: 15 + -15 = 0
0 + w = -28.722813233 + -15
w = -28.722813233 + -15

Combine like terms: -28.722813233 + -15 = -43.722813233
w = -43.722813233

Simplifying
w = -43.722813233


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {13.722813233, -43.722813233}

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