4w^2-80w+400=200

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Solution for 4w^2-80w+400=200 equation: 


Simplifying
4w2 + -80w + 400 = 200

Reorder the terms:
400 + -80w + 4w2 = 200

Solving
400 + -80w + 4w2 = 200

Solving for variable 'w'.

Reorder the terms:
400 + -200 + -80w + 4w2 = 200 + -200

Combine like terms: 400 + -200 = 200
200 + -80w + 4w2 = 200 + -200

Combine like terms: 200 + -200 = 0
200 + -80w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(50 + -20w + w2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(50 + -20w + w2)' equal to zero and attempt to solve:

Simplifying
50 + -20w + w2 = 0

Solving
50 + -20w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -20w + -50 + w2 = 0 + -50

Reorder the terms:
50 + -50 + -20w + w2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -20w + w2 = 0 + -50
-20w + w2 = 0 + -50

Combine like terms: 0 + -50 = -50
-20w + w2 = -50

The w term is -20w.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20w + 100 + w2 = -50 + 100

Reorder the terms:
100 + -20w + w2 = -50 + 100

Combine like terms: -50 + 100 = 50
100 + -20w + w2 = 50

Factor a perfect square on the left side:
(w + -10)(w + -10) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(w + -10) equal to 7.071067812 and -7.071067812.


Subproblem 1
w + -10 = 7.071067812

Simplifying
w + -10 = 7.071067812

Reorder the terms:
-10 + w = 7.071067812

Solving
-10 + w = 7.071067812

Solving for variable 'w'.

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

Add '10' to each side of the equation.
-10 + 10 + w = 7.071067812 + 10

Combine like terms: -10 + 10 = 0
0 + w = 7.071067812 + 10
w = 7.071067812 + 10

Combine like terms: 7.071067812 + 10 = 17.071067812
w = 17.071067812

Simplifying
w = 17.071067812


Subproblem 2
w + -10 = -7.071067812

Simplifying
w + -10 = -7.071067812

Reorder the terms:
-10 + w = -7.071067812

Solving
-10 + w = -7.071067812

Solving for variable 'w'.

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

Add '10' to each side of the equation.
-10 + 10 + w = -7.071067812 + 10

Combine like terms: -10 + 10 = 0
0 + w = -7.071067812 + 10
w = -7.071067812 + 10

Combine like terms: -7.071067812 + 10 = 2.928932188
w = 2.928932188

Simplifying
w = 2.928932188


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {17.071067812, 2.928932188}
Solution
w = {17.071067812, 2.928932188}

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