2w^2+14w+13=2w+25

Solution for 2w^2+14w+13=2w+25 equation:

Simplifying
2w2 + 14w + 13 = 2w + 25

Reorder the terms:
13 + 14w + 2w2 = 2w + 25

Reorder the terms:
13 + 14w + 2w2 = 25 + 2w

Solving
13 + 14w + 2w2 = 25 + 2w

Solving for variable 'w'.

Reorder the terms:
13 + -25 + 14w + -2w + 2w2 = 25 + 2w + -25 + -2w

Combine like terms: 13 + -25 = -12
-12 + 14w + -2w + 2w2 = 25 + 2w + -25 + -2w

Combine like terms: 14w + -2w = 12w
-12 + 12w + 2w2 = 25 + 2w + -25 + -2w

Reorder the terms:
-12 + 12w + 2w2 = 25 + -25 + 2w + -2w

Combine like terms: 25 + -25 = 0
-12 + 12w + 2w2 = 0 + 2w + -2w
-12 + 12w + 2w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-12 + 12w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 6w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 6w + w2)' equal to zero and attempt to solve:

Simplifying
-6 + 6w + w2 = 0

Solving
-6 + 6w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + 6w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6w + w2 = 0 + 6
6w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
6w + w2 = 6

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 6 + 9

Reorder the terms:
9 + 6w + w2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6w + w2 = 15

Factor a perfect square on the left side:
(w + 3)(w + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(w + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1
w + 3 = 3.872983346

Simplifying
w + 3 = 3.872983346

Reorder the terms:
3 + w = 3.872983346

Solving
3 + w = 3.872983346

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + w = 3.872983346 + -3
w = 3.872983346 + -3

Combine like terms: 3.872983346 + -3 = 0.872983346
w = 0.872983346

Simplifying
w = 0.872983346

Subproblem 2
w + 3 = -3.872983346

Simplifying
w + 3 = -3.872983346

Reorder the terms:
3 + w = -3.872983346

Solving
3 + w = -3.872983346

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -3.872983346 + -3

Combine like terms: 3 + -3 = 0
0 + w = -3.872983346 + -3
w = -3.872983346 + -3

Combine like terms: -3.872983346 + -3 = -6.872983346
w = -6.872983346

Simplifying
w = -6.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.872983346, -6.872983346}
Solution
w = {0.872983346, -6.872983346}