w^2-10w-4=0

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Solution for w^2-10w-4=0 equation: 


Simplifying
w2 + -10w + -4 = 0

Reorder the terms:
-4 + -10w + w2 = 0

Solving
-4 + -10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -10w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -10w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -10w + w2 = 0 + 4
-10w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-10w + w2 = 4

The w term is -10w.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10w + 25 + w2 = 4 + 25

Reorder the terms:
25 + -10w + w2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + -10w + w2 = 29

Factor a perfect square on the left side:
(w + -5)(w + -5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(w + -5) equal to 5.385164807 and -5.385164807.


Subproblem 1
w + -5 = 5.385164807

Simplifying
w + -5 = 5.385164807

Reorder the terms:
-5 + w = 5.385164807

Solving
-5 + w = 5.385164807

Solving for variable 'w'.

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

Add '5' to each side of the equation.
-5 + 5 + w = 5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + w = 5.385164807 + 5
w = 5.385164807 + 5

Combine like terms: 5.385164807 + 5 = 10.385164807
w = 10.385164807

Simplifying
w = 10.385164807


Subproblem 2
w + -5 = -5.385164807

Simplifying
w + -5 = -5.385164807

Reorder the terms:
-5 + w = -5.385164807

Solving
-5 + w = -5.385164807

Solving for variable 'w'.

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

Add '5' to each side of the equation.
-5 + 5 + w = -5.385164807 + 5

Combine like terms: -5 + 5 = 0
0 + w = -5.385164807 + 5
w = -5.385164807 + 5

Combine like terms: -5.385164807 + 5 = -0.385164807
w = -0.385164807

Simplifying
w = -0.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {10.385164807, -0.385164807}

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