2w^2+2w+21+w^2+8w+8=0

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Solution for 2w^2+2w+21+w^2+8w+8=0 equation: 


Simplifying
2w2 + 2w + 21 + w2 + 8w + 8 = 0

Reorder the terms:
21 + 8 + 2w + 8w + 2w2 + w2 = 0

Combine like terms: 21 + 8 = 29
29 + 2w + 8w + 2w2 + w2 = 0

Combine like terms: 2w + 8w = 10w
29 + 10w + 2w2 + w2 = 0

Combine like terms: 2w2 + w2 = 3w2
29 + 10w + 3w2 = 0

Solving
29 + 10w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
9.666666667 + 3.333333333w + w2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + 3.333333333w + -9.666666667 + w2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + 3.333333333w + w2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + 3.333333333w + w2 = 0 + -9.666666667
3.333333333w + w2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
3.333333333w + w2 = -9.666666667

The w term is 3.333333333w.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333w + 2.777777779 + w2 = -9.666666667 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333w + w2 = -9.666666667 + 2.777777779

Combine like terms: -9.666666667 + 2.777777779 = -6.888888888
2.777777779 + 3.333333333w + w2 = -6.888888888

Factor a perfect square on the left side:
(w + 1.666666667)(w + 1.666666667) = -6.888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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