10w^2-44w-400=0

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Solution for 10w^2-44w-400=0 equation: 


Simplifying
10w2 + -44w + -400 = 0

Reorder the terms:
-400 + -44w + 10w2 = 0

Solving
-400 + -44w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + -22w + 5w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-200 + -22w + 5w2)' equal to zero and attempt to solve:

Simplifying
-200 + -22w + 5w2 = 0

Solving
-200 + -22w + 5w2 = 0

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

Divide each side by '5'.
-40 + -4.4w + w2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -4.4w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + -4.4w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -4.4w + w2 = 0 + 40
-4.4w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
-4.4w + w2 = 40

The w term is -4.4w.  Take half its coefficient (-2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
-4.4w + 4.84 + w2 = 40 + 4.84

Reorder the terms:
4.84 + -4.4w + w2 = 40 + 4.84

Combine like terms: 40 + 4.84 = 44.84
4.84 + -4.4w + w2 = 44.84

Factor a perfect square on the left side:
(w + -2.2)(w + -2.2) = 44.84

Calculate the square root of the right side: 6.696267617

Break this problem into two subproblems by setting 
(w + -2.2) equal to 6.696267617 and -6.696267617.


Subproblem 1
w + -2.2 = 6.696267617

Simplifying
w + -2.2 = 6.696267617

Reorder the terms:
-2.2 + w = 6.696267617

Solving
-2.2 + w = 6.696267617

Solving for variable 'w'.

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

Add '2.2' to each side of the equation.
-2.2 + 2.2 + w = 6.696267617 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + w = 6.696267617 + 2.2
w = 6.696267617 + 2.2

Combine like terms: 6.696267617 + 2.2 = 8.896267617
w = 8.896267617

Simplifying
w = 8.896267617


Subproblem 2
w + -2.2 = -6.696267617

Simplifying
w + -2.2 = -6.696267617

Reorder the terms:
-2.2 + w = -6.696267617

Solving
-2.2 + w = -6.696267617

Solving for variable 'w'.

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

Add '2.2' to each side of the equation.
-2.2 + 2.2 + w = -6.696267617 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + w = -6.696267617 + 2.2
w = -6.696267617 + 2.2

Combine like terms: -6.696267617 + 2.2 = -4.496267617
w = -4.496267617

Simplifying
w = -4.496267617


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.896267617, -4.496267617}
Solution
w = {8.896267617, -4.496267617}

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