18w^2+10w+1=0

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Solution for 18w^2+10w+1=0 equation: 


Simplifying
18w2 + 10w + 1 = 0

Reorder the terms:
1 + 10w + 18w2 = 0

Solving
1 + 10w + 18w2 = 0

Solving for variable 'w'.

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

Divide each side by '18'.
0.05555555556 + 0.5555555556w + w2 = 0

Move the constant term to the right:

Add '-0.05555555556' to each side of the equation.
0.05555555556 + 0.5555555556w + -0.05555555556 + w2 = 0 + -0.05555555556

Reorder the terms:
0.05555555556 + -0.05555555556 + 0.5555555556w + w2 = 0 + -0.05555555556

Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000
0.00000000000 + 0.5555555556w + w2 = 0 + -0.05555555556
0.5555555556w + w2 = 0 + -0.05555555556

Combine like terms: 0 + -0.05555555556 = -0.05555555556
0.5555555556w + w2 = -0.05555555556

The w term is 0.5555555556w.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556w + 0.07716049384 + w2 = -0.05555555556 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556w + w2 = -0.05555555556 + 0.07716049384

Combine like terms: -0.05555555556 + 0.07716049384 = 0.02160493828
0.07716049384 + 0.5555555556w + w2 = 0.02160493828

Factor a perfect square on the left side:
(w + 0.2777777778)(w + 0.2777777778) = 0.02160493828

Calculate the square root of the right side: 0.146986184

Break this problem into two subproblems by setting 
(w + 0.2777777778) equal to 0.146986184 and -0.146986184.


Subproblem 1
w + 0.2777777778 = 0.146986184

Simplifying
w + 0.2777777778 = 0.146986184

Reorder the terms:
0.2777777778 + w = 0.146986184

Solving
0.2777777778 + w = 0.146986184

Solving for variable 'w'.

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

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + w = 0.146986184 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + w = 0.146986184 + -0.2777777778
w = 0.146986184 + -0.2777777778

Combine like terms: 0.146986184 + -0.2777777778 = -0.1307915938
w = -0.1307915938

Simplifying
w = -0.1307915938


Subproblem 2
w + 0.2777777778 = -0.146986184

Simplifying
w + 0.2777777778 = -0.146986184

Reorder the terms:
0.2777777778 + w = -0.146986184

Solving
0.2777777778 + w = -0.146986184

Solving for variable 'w'.

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

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + w = -0.146986184 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + w = -0.146986184 + -0.2777777778
w = -0.146986184 + -0.2777777778

Combine like terms: -0.146986184 + -0.2777777778 = -0.4247639618
w = -0.4247639618

Simplifying
w = -0.4247639618


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.1307915938, -0.4247639618}

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