99999999999999999w^2-9999999999w+9999999=99999999

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Solution for 99999999999999999w^2-9999999999w+9999999=99999999 equation: 


Simplifying
99999999999999999w2 + -9999999999w + 9999999 = 99999999

Reorder the terms:
9999999 + -9999999999w + 99999999999999999w2 = 99999999

Solving
9999999 + -9999999999w + 99999999999999999w2 = 99999999

Solving for variable 'w'.

Reorder the terms:
9999999 + -99999999 + -9999999999w + 99999999999999999w2 = 99999999 + -99999999

Combine like terms: 9999999 + -99999999 = -90000000
-90000000 + -9999999999w + 99999999999999999w2 = 99999999 + -99999999

Combine like terms: 99999999 + -99999999 = 0
-90000000 + -9999999999w + 99999999999999999w2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-10000000 + -1111111111w + 11111111110000000w2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-10000000 + -1111111111w + 11111111110000000w2)' equal to zero and attempt to solve:

Simplifying
-10000000 + -1111111111w + 11111111110000000w2 = 0

Solving
-10000000 + -1111111111w + 11111111110000000w2 = 0

Begin completing the square.  Divide all terms by
11111111110000000 the coefficient of the squared term: 

Divide each side by '11111111110000000'.
-0.0000000009000000001 + -0.0000001w + w2 = 0.0000000

Move the constant term to the right:

Add '0.0000000009000000001' to each side of the equation.
-0.0000000009000000001 + -0.0000001w + 0.0000000009000000001 + w2 = 0.0000000 + 0.0000000009000000001

Reorder the terms:
-0.0000000009000000001 + 0.0000000009000000001 + -0.0000001w + w2 = 0.0000000 + 0.0000000009000000001

Combine like terms: -0.0000000009000000001 + 0.0000000009000000001 = 0.0000000000000000000
0.0000000000000000000 + -0.0000001w + w2 = 0.0000000 + 0.0000000009000000001
-0.0000001w + w2 = 0.0000000 + 0.0000000009000000001

Combine like terms: 0.0000000 + 0.0000000009000000001 = 0.0000000009000000001
-0.0000001w + w2 = 0.0000000009000000001

The w term is -0.0000001w.  Take half its coefficient (-0.00000005).
Square it (0.0000000000000025) and add it to both sides.

Add '0.0000000000000025' to each side of the equation.
-0.0000001w + 0.0000000000000025 + w2 = 0.0000000009000000001 + 0.0000000000000025

Reorder the terms:
0.0000000000000025 + -0.0000001w + w2 = 0.0000000009000000001 + 0.0000000000000025

Combine like terms: 0.0000000009000000001 + 0.0000000000000025 = 0.0000000009000025001
0.0000000000000025 + -0.0000001w + w2 = 0.0000000009000025001

Factor a perfect square on the left side:
(w + -0.00000005)(w + -0.00000005) = 0.0000000009000025001

Calculate the square root of the right side: 0.00003

Break this problem into two subproblems by setting 
(w + -0.00000005) equal to 0.00003 and -0.00003.


Subproblem 1
w + -0.00000005 = 0.00003

Simplifying
w + -0.00000005 = 0.00003

Reorder the terms:
-0.00000005 + w = 0.00003

Solving
-0.00000005 + w = 0.00003

Solving for variable 'w'.

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

Add '0.00000005' to each side of the equation.
-0.00000005 + 0.00000005 + w = 0.00003 + 0.00000005

Combine like terms: -0.00000005 + 0.00000005 = 0.00000000
0.00000000 + w = 0.00003 + 0.00000005
w = 0.00003 + 0.00000005

Combine like terms: 0.00003 + 0.00000005 = 0.00003005
w = 0.00003005

Simplifying
w = 0.00003005


Subproblem 2
w + -0.00000005 = -0.00003

Simplifying
w + -0.00000005 = -0.00003

Reorder the terms:
-0.00000005 + w = -0.00003

Solving
-0.00000005 + w = -0.00003

Solving for variable 'w'.

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

Add '0.00000005' to each side of the equation.
-0.00000005 + 0.00000005 + w = -0.00003 + 0.00000005

Combine like terms: -0.00000005 + 0.00000005 = 0.00000000
0.00000000 + w = -0.00003 + 0.00000005
w = -0.00003 + 0.00000005

Combine like terms: -0.00003 + 0.00000005 = -0.00002995
w = -0.00002995

Simplifying
w = -0.00002995


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.00003005, -0.00002995}
Solution
w = {0.00003005, -0.00002995}

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