w^2+3w=5

Solution for w^2+3w=5 equation:

Simplifying
w2 + 3w = 5

Reorder the terms:
3w + w2 = 5

Solving
3w + w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + 3w + w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3w + 5 + w2 = 0 + 5

Reorder the terms:
-5 + 5 + 3w + w2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3w + w2 = 0 + 5
3w + w2 = 0 + 5

Combine like terms: 0 + 5 = 5
3w + w2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3w + w2 = 7.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(w + 1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
w + 1.5 = 2.692582404

Simplifying
w + 1.5 = 2.692582404

Reorder the terms:
1.5 + w = 2.692582404

Solving
1.5 + w = 2.692582404

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 = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 2.692582404 + -1.5
w = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
w = 1.192582404

Simplifying
w = 1.192582404

Subproblem 2
w + 1.5 = -2.692582404

Simplifying
w + 1.5 = -2.692582404

Reorder the terms:
1.5 + w = -2.692582404

Solving
1.5 + w = -2.692582404

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 = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -2.692582404 + -1.5
w = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
w = -4.192582404

Simplifying
w = -4.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.192582404, -4.192582404}