2w^2-4w-20=0

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Solution for 2w^2-4w-20=0 equation:


Simplifying
2w2 + -4w + -20 = 0

Reorder the terms:
-20 + -4w + 2w2 = 0

Solving
-20 + -4w + 2w2 = 0

Solving for variable 'w'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-10 + -2w + w2 = 0

Solving
-10 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2w + 10 + w2 = 0 + 10

Reorder the terms:
-10 + 10 + -2w + w2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2w + w2 = 0 + 10
-2w + w2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2w + w2 = 10

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 10 + 1

Reorder the terms:
1 + -2w + w2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2w + w2 = 11

Factor a perfect square on the left side:
(w + -1)(w + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(w + -1) equal to 3.31662479 and -3.31662479.


Subproblem 1
w + -1 = 3.31662479

Simplifying
w + -1 = 3.31662479

Reorder the terms:
-1 + w = 3.31662479

Solving
-1 + w = 3.31662479

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + w = 3.31662479 + 1
w = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
w = 4.31662479

Simplifying
w = 4.31662479


Subproblem 2
w + -1 = -3.31662479

Simplifying
w + -1 = -3.31662479

Reorder the terms:
-1 + w = -3.31662479

Solving
-1 + w = -3.31662479

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + w = -3.31662479 + 1
w = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
w = -2.31662479

Simplifying
w = -2.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.31662479, -2.31662479}
Solution
w = {4.31662479, -2.31662479}

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