3(w-4)(w-4)=34

Solution for 3(w-4)(w-4)=34 equation:

Simplifying
3(w + -4)(w + -4) = 34

Reorder the terms:
3(-4 + w)(w + -4) = 34

Reorder the terms:
3(-4 + w)(-4 + w) = 34

Multiply (-4 + w) * (-4 + w)
3(-4(-4 + w) + w(-4 + w)) = 34
3((-4 * -4 + w * -4) + w(-4 + w)) = 34
3((16 + -4w) + w(-4 + w)) = 34
3(16 + -4w + (-4 * w + w * w)) = 34
3(16 + -4w + (-4w + w2)) = 34

Combine like terms: -4w + -4w = -8w
3(16 + -8w + w2) = 34
(16 * 3 + -8w * 3 + w2 * 3) = 34
(48 + -24w + 3w2) = 34

Solving
48 + -24w + 3w2 = 34

Solving for variable 'w'.

Reorder the terms:
48 + -34 + -24w + 3w2 = 34 + -34

Combine like terms: 48 + -34 = 14
14 + -24w + 3w2 = 34 + -34

Combine like terms: 34 + -34 = 0
14 + -24w + 3w2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
4.666666667 + -8w + w2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -8w + -4.666666667 + w2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -8w + w2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -8w + w2 = 0 + -4.666666667
-8w + w2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-8w + w2 = -4.666666667

The w term is -8w.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8w + 16 + w2 = -4.666666667 + 16

Reorder the terms:
16 + -8w + w2 = -4.666666667 + 16

Combine like terms: -4.666666667 + 16 = 11.333333333
16 + -8w + w2 = 11.333333333

Factor a perfect square on the left side:
(w + -4)(w + -4) = 11.333333333

Calculate the square root of the right side: 3.366501646

Break this problem into two subproblems by setting 
(w + -4) equal to 3.366501646 and -3.366501646.

Subproblem 1
w + -4 = 3.366501646

Simplifying
w + -4 = 3.366501646

Reorder the terms:
-4 + w = 3.366501646

Solving
-4 + w = 3.366501646

Solving for variable 'w'.

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

Add '4' to each side of the equation.
-4 + 4 + w = 3.366501646 + 4

Combine like terms: -4 + 4 = 0
0 + w = 3.366501646 + 4
w = 3.366501646 + 4

Combine like terms: 3.366501646 + 4 = 7.366501646
w = 7.366501646

Simplifying
w = 7.366501646

Subproblem 2
w + -4 = -3.366501646

Simplifying
w + -4 = -3.366501646

Reorder the terms:
-4 + w = -3.366501646

Solving
-4 + w = -3.366501646

Solving for variable 'w'.

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

Add '4' to each side of the equation.
-4 + 4 + w = -3.366501646 + 4

Combine like terms: -4 + 4 = 0
0 + w = -3.366501646 + 4
w = -3.366501646 + 4

Combine like terms: -3.366501646 + 4 = 0.633498354
w = 0.633498354

Simplifying
w = 0.633498354

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.366501646, 0.633498354}