3w^2-30w+30=0

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Solution for 3w^2-30w+30=0 equation: 


Simplifying
3w2 + -30w + 30 = 0

Reorder the terms:
30 + -30w + 3w2 = 0

Solving
30 + -30w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + -10w + w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + -10w + w2)' equal to zero and attempt to solve:

Simplifying
10 + -10w + w2 = 0

Solving
10 + -10w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -10w + -10 + w2 = 0 + -10

Reorder the terms:
10 + -10 + -10w + w2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -10w + w2 = 0 + -10
-10w + w2 = 0 + -10

Combine like terms: 0 + -10 = -10
-10w + w2 = -10

The w term is -10w.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10w + 25 + w2 = -10 + 25

Reorder the terms:
25 + -10w + w2 = -10 + 25

Combine like terms: -10 + 25 = 15
25 + -10w + w2 = 15

Factor a perfect square on the left side:
(w + -5)(w + -5) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(w + -5) equal to 3.872983346 and -3.872983346.


Subproblem 1
w + -5 = 3.872983346

Simplifying
w + -5 = 3.872983346

Reorder the terms:
-5 + w = 3.872983346

Solving
-5 + w = 3.872983346

Solving for variable 'w'.

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

Add '5' to each side of the equation.
-5 + 5 + w = 3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + w = 3.872983346 + 5
w = 3.872983346 + 5

Combine like terms: 3.872983346 + 5 = 8.872983346
w = 8.872983346

Simplifying
w = 8.872983346


Subproblem 2
w + -5 = -3.872983346

Simplifying
w + -5 = -3.872983346

Reorder the terms:
-5 + w = -3.872983346

Solving
-5 + w = -3.872983346

Solving for variable 'w'.

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

Add '5' to each side of the equation.
-5 + 5 + w = -3.872983346 + 5

Combine like terms: -5 + 5 = 0
0 + w = -3.872983346 + 5
w = -3.872983346 + 5

Combine like terms: -3.872983346 + 5 = 1.127016654
w = 1.127016654

Simplifying
w = 1.127016654


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.872983346, 1.127016654}
Solution
w = {8.872983346, 1.127016654}

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