(2w-6)(w)=6400

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Solution for (2w-6)(w)=6400 equation: 


Simplifying
(2w + -6)(w) = 6400

Reorder the terms:
(-6 + 2w)(w) = 6400

Reorder the terms for easier multiplication:
w(-6 + 2w) = 6400
(-6 * w + 2w * w) = 6400
(-6w + 2w2) = 6400

Solving
-6w + 2w2 = 6400

Solving for variable 'w'.

Reorder the terms:
-6400 + -6w + 2w2 = 6400 + -6400

Combine like terms: 6400 + -6400 = 0
-6400 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3200 + -3w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3200 + -3w + w2)' equal to zero and attempt to solve:

Simplifying
-3200 + -3w + w2 = 0

Solving
-3200 + -3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3200' to each side of the equation.
-3200 + -3w + 3200 + w2 = 0 + 3200

Reorder the terms:
-3200 + 3200 + -3w + w2 = 0 + 3200

Combine like terms: -3200 + 3200 = 0
0 + -3w + w2 = 0 + 3200
-3w + w2 = 0 + 3200

Combine like terms: 0 + 3200 = 3200
-3w + w2 = 3200

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = 3200 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 3200 + 2.25

Combine like terms: 3200 + 2.25 = 3202.25
2.25 + -3w + w2 = 3202.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 3202.25

Calculate the square root of the right side: 56.588426379

Break this problem into two subproblems by setting 
(w + -1.5) equal to 56.588426379 and -56.588426379.


Subproblem 1
w + -1.5 = 56.588426379

Simplifying
w + -1.5 = 56.588426379

Reorder the terms:
-1.5 + w = 56.588426379

Solving
-1.5 + w = 56.588426379

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = 56.588426379 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = 56.588426379 + 1.5
w = 56.588426379 + 1.5

Combine like terms: 56.588426379 + 1.5 = 58.088426379
w = 58.088426379

Simplifying
w = 58.088426379


Subproblem 2
w + -1.5 = -56.588426379

Simplifying
w + -1.5 = -56.588426379

Reorder the terms:
-1.5 + w = -56.588426379

Solving
-1.5 + w = -56.588426379

Solving for variable 'w'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + w = -56.588426379 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = -56.588426379 + 1.5
w = -56.588426379 + 1.5

Combine like terms: -56.588426379 + 1.5 = -55.088426379
w = -55.088426379

Simplifying
w = -55.088426379


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {58.088426379, -55.088426379}
Solution
w = {58.088426379, -55.088426379}

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