w^2+3w-49=0

Solution for w^2+3w-49=0 equation:

Simplifying
w2 + 3w + -49 = 0

Reorder the terms:
-49 + 3w + w2 = 0

Solving
-49 + 3w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 3w + 49 + w2 = 0 + 49

Reorder the terms:
-49 + 49 + 3w + w2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 3w + w2 = 0 + 49
3w + w2 = 0 + 49

Combine like terms: 0 + 49 = 49
3w + w2 = 49

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 49 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 49 + 2.25

Combine like terms: 49 + 2.25 = 51.25
2.25 + 3w + w2 = 51.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(w + 1.5) equal to 7.158910532 and -7.158910532.

Subproblem 1
w + 1.5 = 7.158910532

Simplifying
w + 1.5 = 7.158910532

Reorder the terms:
1.5 + w = 7.158910532

Solving
1.5 + w = 7.158910532

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 7.158910532 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 7.158910532 + -1.5
w = 7.158910532 + -1.5

Combine like terms: 7.158910532 + -1.5 = 5.658910532
w = 5.658910532

Simplifying
w = 5.658910532

Subproblem 2
w + 1.5 = -7.158910532

Simplifying
w + 1.5 = -7.158910532

Reorder the terms:
1.5 + w = -7.158910532

Solving
1.5 + w = -7.158910532

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -7.158910532 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -7.158910532 + -1.5
w = -7.158910532 + -1.5

Combine like terms: -7.158910532 + -1.5 = -8.658910532
w = -8.658910532

Simplifying
w = -8.658910532

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.658910532, -8.658910532}