-2(w-7)10w=34

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Solution for -2(w-7)10w=34 equation: 


Simplifying
-2(w + -7) * 10w = 34

Reorder the terms:
-2(-7 + w) * 10w = 34

Reorder the terms for easier multiplication:
-2 * 10w(-7 + w) = 34

Multiply -2 * 10
-20w(-7 + w) = 34
(-7 * -20w + w * -20w) = 34
(140w + -20w2) = 34

Solving
140w + -20w2 = 34

Solving for variable 'w'.

Reorder the terms:
-34 + 140w + -20w2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 140w + -20w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 70w + -10w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 70w + -10w2)' equal to zero and attempt to solve:

Simplifying
-17 + 70w + -10w2 = 0

Solving
-17 + 70w + -10w2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
1.7 + -7w + w2 = 0.0

Move the constant term to the right:

Add '-1.7' to each side of the equation.
1.7 + -7w + -1.7 + w2 = 0.0 + -1.7

Reorder the terms:
1.7 + -1.7 + -7w + w2 = 0.0 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + -7w + w2 = 0.0 + -1.7
-7w + w2 = 0.0 + -1.7

Combine like terms: 0.0 + -1.7 = -1.7
-7w + w2 = -1.7

The w term is -7w.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7w + 12.25 + w2 = -1.7 + 12.25

Reorder the terms:
12.25 + -7w + w2 = -1.7 + 12.25

Combine like terms: -1.7 + 12.25 = 10.55
12.25 + -7w + w2 = 10.55

Factor a perfect square on the left side:
(w + -3.5)(w + -3.5) = 10.55

Calculate the square root of the right side: 3.248076354

Break this problem into two subproblems by setting 
(w + -3.5) equal to 3.248076354 and -3.248076354.


Subproblem 1
w + -3.5 = 3.248076354

Simplifying
w + -3.5 = 3.248076354

Reorder the terms:
-3.5 + w = 3.248076354

Solving
-3.5 + w = 3.248076354

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = 3.248076354 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = 3.248076354 + 3.5
w = 3.248076354 + 3.5

Combine like terms: 3.248076354 + 3.5 = 6.748076354
w = 6.748076354

Simplifying
w = 6.748076354


Subproblem 2
w + -3.5 = -3.248076354

Simplifying
w + -3.5 = -3.248076354

Reorder the terms:
-3.5 + w = -3.248076354

Solving
-3.5 + w = -3.248076354

Solving for variable 'w'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + w = -3.248076354 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + w = -3.248076354 + 3.5
w = -3.248076354 + 3.5

Combine like terms: -3.248076354 + 3.5 = 0.251923646
w = 0.251923646

Simplifying
w = 0.251923646


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.748076354, 0.251923646}
Solution
w = {6.748076354, 0.251923646}

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