2w^2+11w+39=7w+w+7w+49

Solution for 2w^2+11w+39=7w+w+7w+49 equation:

Simplifying
2w2 + 11w + 39 = 7w + w + 7w + 49

Reorder the terms:
39 + 11w + 2w2 = 7w + w + 7w + 49

Reorder the terms:
39 + 11w + 2w2 = 49 + 7w + w + 7w

Combine like terms: 7w + w = 8w
39 + 11w + 2w2 = 49 + 8w + 7w

Combine like terms: 8w + 7w = 15w
39 + 11w + 2w2 = 49 + 15w

Solving
39 + 11w + 2w2 = 49 + 15w

Solving for variable 'w'.

Reorder the terms:
39 + -49 + 11w + -15w + 2w2 = 49 + 15w + -49 + -15w

Combine like terms: 39 + -49 = -10
-10 + 11w + -15w + 2w2 = 49 + 15w + -49 + -15w

Combine like terms: 11w + -15w = -4w
-10 + -4w + 2w2 = 49 + 15w + -49 + -15w

Reorder the terms:
-10 + -4w + 2w2 = 49 + -49 + 15w + -15w

Combine like terms: 49 + -49 = 0
-10 + -4w + 2w2 = 0 + 15w + -15w
-10 + -4w + 2w2 = 15w + -15w

Combine like terms: 15w + -15w = 0
-10 + -4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -2w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-5 + -2w + w2 = 0

Solving
-5 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2w + 5 + w2 = 0 + 5

Reorder the terms:
-5 + 5 + -2w + w2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2w + w2 = 0 + 5
-2w + w2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2w + w2 = 5

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 5 + 1

Reorder the terms:
1 + -2w + w2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2w + w2 = 6

Factor a perfect square on the left side:
(w + -1)(w + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(w + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
w + -1 = 2.449489743

Simplifying
w + -1 = 2.449489743

Reorder the terms:
-1 + w = 2.449489743

Solving
-1 + w = 2.449489743

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + w = 2.449489743 + 1
w = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
w = 3.449489743

Simplifying
w = 3.449489743

Subproblem 2
w + -1 = -2.449489743

Simplifying
w + -1 = -2.449489743

Reorder the terms:
-1 + w = -2.449489743

Solving
-1 + w = -2.449489743

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + w = -2.449489743 + 1
w = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
w = -1.449489743

Simplifying
w = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.449489743, -1.449489743}
Solution
w = {3.449489743, -1.449489743}