(2w^2-5w+1)+(-6w^2+4w+7)=

Solution for (2w^2-5w+1)+(-6w^2+4w+7)= equation:

Simplifying
(2w2 + -5w + 1) + (-6w2 + 4w + 7) = 0

Reorder the terms:
(1 + -5w + 2w2) + (-6w2 + 4w + 7) = 0

Remove parenthesis around (1 + -5w + 2w2)
1 + -5w + 2w2 + (-6w2 + 4w + 7) = 0

Reorder the terms:
1 + -5w + 2w2 + (7 + 4w + -6w2) = 0

Remove parenthesis around (7 + 4w + -6w2)
1 + -5w + 2w2 + 7 + 4w + -6w2 = 0

Reorder the terms:
1 + 7 + -5w + 4w + 2w2 + -6w2 = 0

Combine like terms: 1 + 7 = 8
8 + -5w + 4w + 2w2 + -6w2 = 0

Combine like terms: -5w + 4w = -1w
8 + -1w + 2w2 + -6w2 = 0

Combine like terms: 2w2 + -6w2 = -4w2
8 + -1w + -4w2 = 0

Solving
8 + -1w + -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'.
-2 + 0.25w + w2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.25w + 2 + w2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.25w + w2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.25w + w2 = 0 + 2
0.25w + w2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.25w + w2 = 2

The w term is 0.25w.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25w + 0.015625 + w2 = 2 + 0.015625

Reorder the terms:
0.015625 + 0.25w + w2 = 2 + 0.015625

Combine like terms: 2 + 0.015625 = 2.015625
0.015625 + 0.25w + w2 = 2.015625

Factor a perfect square on the left side:
(w + 0.125)(w + 0.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(w + 0.125) equal to 1.419727086 and -1.419727086.

Subproblem 1
w + 0.125 = 1.419727086

Simplifying
w + 0.125 = 1.419727086

Reorder the terms:
0.125 + w = 1.419727086

Solving
0.125 + w = 1.419727086

Solving for variable 'w'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + w = 1.419727086 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + w = 1.419727086 + -0.125
w = 1.419727086 + -0.125

Combine like terms: 1.419727086 + -0.125 = 1.294727086
w = 1.294727086

Simplifying
w = 1.294727086

Subproblem 2
w + 0.125 = -1.419727086

Simplifying
w + 0.125 = -1.419727086

Reorder the terms:
0.125 + w = -1.419727086

Solving
0.125 + w = -1.419727086

Solving for variable 'w'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + w = -1.419727086 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + w = -1.419727086 + -0.125
w = -1.419727086 + -0.125

Combine like terms: -1.419727086 + -0.125 = -1.544727086
w = -1.544727086

Simplifying
w = -1.544727086

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.294727086, -1.544727086}