-4w^2+46w-50=0

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Solution for -4w^2+46w-50=0 equation: 


Simplifying
-4w2 + 46w + -50 = 0

Reorder the terms:
-50 + 46w + -4w2 = 0

Solving
-50 + 46w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 23w + -2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 23w + -2w2)' equal to zero and attempt to solve:

Simplifying
-25 + 23w + -2w2 = 0

Solving
-25 + 23w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
12.5 + -11.5w + w2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -11.5w + -12.5 + w2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -11.5w + w2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -11.5w + w2 = 0 + -12.5
-11.5w + w2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-11.5w + w2 = -12.5

The w term is -11.5w.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5w + 33.0625 + w2 = -12.5 + 33.0625

Reorder the terms:
33.0625 + -11.5w + w2 = -12.5 + 33.0625

Combine like terms: -12.5 + 33.0625 = 20.5625
33.0625 + -11.5w + w2 = 20.5625

Factor a perfect square on the left side:
(w + -5.75)(w + -5.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(w + -5.75) equal to 4.534589287 and -4.534589287.


Subproblem 1
w + -5.75 = 4.534589287

Simplifying
w + -5.75 = 4.534589287

Reorder the terms:
-5.75 + w = 4.534589287

Solving
-5.75 + w = 4.534589287

Solving for variable 'w'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + w = 4.534589287 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + w = 4.534589287 + 5.75
w = 4.534589287 + 5.75

Combine like terms: 4.534589287 + 5.75 = 10.284589287
w = 10.284589287

Simplifying
w = 10.284589287


Subproblem 2
w + -5.75 = -4.534589287

Simplifying
w + -5.75 = -4.534589287

Reorder the terms:
-5.75 + w = -4.534589287

Solving
-5.75 + w = -4.534589287

Solving for variable 'w'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + w = -4.534589287 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + w = -4.534589287 + 5.75
w = -4.534589287 + 5.75

Combine like terms: -4.534589287 + 5.75 = 1.215410713
w = 1.215410713

Simplifying
w = 1.215410713


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.284589287, 1.215410713}
Solution
w = {10.284589287, 1.215410713}

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