0.36w^2+0.84w+0.49=0

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Solution for 0.36w^2+0.84w+0.49=0 equation: 


Simplifying
0.36w2 + 0.84w + 0.49 = 0

Reorder the terms:
0.49 + 0.84w + 0.36w2 = 0

Solving
0.49 + 0.84w + 0.36w2 = 0

Solving for variable 'w'.

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

Divide each side by '0.36'.
1.361111111 + 2.333333333w + w2 = 0

Move the constant term to the right:

Add '-1.361111111' to each side of the equation.
1.361111111 + 2.333333333w + -1.361111111 + w2 = 0 + -1.361111111

Reorder the terms:
1.361111111 + -1.361111111 + 2.333333333w + w2 = 0 + -1.361111111

Combine like terms: 1.361111111 + -1.361111111 = 0.000000000
0.000000000 + 2.333333333w + w2 = 0 + -1.361111111
2.333333333w + w2 = 0 + -1.361111111

Combine like terms: 0 + -1.361111111 = -1.361111111
2.333333333w + w2 = -1.361111111

The w term is 2.333333333w.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333w + 1.361111112 + w2 = -1.361111111 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333w + w2 = -1.361111111 + 1.361111112

Combine like terms: -1.361111111 + 1.361111112 = 0.000000001
1.361111112 + 2.333333333w + w2 = 0.000000001

Factor a perfect square on the left side:
(w + 1.166666667)(w + 1.166666667) = 0.000000001

Calculate the square root of the right side: 0.000031623

Break this problem into two subproblems by setting 
(w + 1.166666667) equal to 0.000031623 and -0.000031623.


Subproblem 1
w + 1.166666667 = 0.000031623

Simplifying
w + 1.166666667 = 0.000031623

Reorder the terms:
1.166666667 + w = 0.000031623

Solving
1.166666667 + w = 0.000031623

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = 0.000031623 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = 0.000031623 + -1.166666667
w = 0.000031623 + -1.166666667

Combine like terms: 0.000031623 + -1.166666667 = -1.166635044
w = -1.166635044

Simplifying
w = -1.166635044


Subproblem 2
w + 1.166666667 = -0.000031623

Simplifying
w + 1.166666667 = -0.000031623

Reorder the terms:
1.166666667 + w = -0.000031623

Solving
1.166666667 + w = -0.000031623

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = -0.000031623 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = -0.000031623 + -1.166666667
w = -0.000031623 + -1.166666667

Combine like terms: -0.000031623 + -1.166666667 = -1.16669829
w = -1.16669829

Simplifying
w = -1.16669829


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.166635044, -1.16669829}

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