(3w^2+4w+5)+(w^2+5w+8)=

Solution for (3w^2+4w+5)+(w^2+5w+8)= equation:

Simplifying
(3w2 + 4w + 5) + (w2 + 5w + 8) = 0

Reorder the terms:
(5 + 4w + 3w2) + (w2 + 5w + 8) = 0

Remove parenthesis around (5 + 4w + 3w2)
5 + 4w + 3w2 + (w2 + 5w + 8) = 0

Reorder the terms:
5 + 4w + 3w2 + (8 + 5w + w2) = 0

Remove parenthesis around (8 + 5w + w2)
5 + 4w + 3w2 + 8 + 5w + w2 = 0

Reorder the terms:
5 + 8 + 4w + 5w + 3w2 + w2 = 0

Combine like terms: 5 + 8 = 13
13 + 4w + 5w + 3w2 + w2 = 0

Combine like terms: 4w + 5w = 9w
13 + 9w + 3w2 + w2 = 0

Combine like terms: 3w2 + w2 = 4w2
13 + 9w + 4w2 = 0

Solving
13 + 9w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
3.25 + 2.25w + w2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + 2.25w + -3.25 + w2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + 2.25w + w2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + 2.25w + w2 = 0 + -3.25
2.25w + w2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
2.25w + w2 = -3.25

The w term is 2.25w.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25w + 1.265625 + w2 = -3.25 + 1.265625

Reorder the terms:
1.265625 + 2.25w + w2 = -3.25 + 1.265625

Combine like terms: -3.25 + 1.265625 = -1.984375
1.265625 + 2.25w + w2 = -1.984375

Factor a perfect square on the left side:
(w + 1.125)(w + 1.125) = -1.984375

Can't calculate square root of the right side.

The solution to this equation could not be determined.