5w*5w+5=-26w

Solution for 5w*5w+5=-26w equation:

Simplifying
5w * 5w + 5 = -26w

Reorder the terms for easier multiplication:
5 * 5w * w + 5 = -26w

Multiply 5 * 5
25w * w + 5 = -26w

Multiply w * w
25w2 + 5 = -26w

Reorder the terms:
5 + 25w2 = -26w

Solving
5 + 25w2 = -26w

Solving for variable 'w'.

Reorder the terms:
5 + 26w + 25w2 = -26w + 26w

Combine like terms: -26w + 26w = 0
5 + 26w + 25w2 = 0

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
0.2 + 1.04w + w2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 1.04w + -0.2 + w2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 1.04w + w2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 1.04w + w2 = 0 + -0.2
1.04w + w2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
1.04w + w2 = -0.2

The w term is 1.04w.  Take half its coefficient (0.52).
Square it (0.2704) and add it to both sides.

Add '0.2704' to each side of the equation.
1.04w + 0.2704 + w2 = -0.2 + 0.2704

Reorder the terms:
0.2704 + 1.04w + w2 = -0.2 + 0.2704

Combine like terms: -0.2 + 0.2704 = 0.0704
0.2704 + 1.04w + w2 = 0.0704

Factor a perfect square on the left side:
(w + 0.52)(w + 0.52) = 0.0704

Calculate the square root of the right side: 0.265329983

Break this problem into two subproblems by setting 
(w + 0.52) equal to 0.265329983 and -0.265329983.

Subproblem 1
w + 0.52 = 0.265329983

Simplifying
w + 0.52 = 0.265329983

Reorder the terms:
0.52 + w = 0.265329983

Solving
0.52 + w = 0.265329983

Solving for variable 'w'.

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

Add '-0.52' to each side of the equation.
0.52 + -0.52 + w = 0.265329983 + -0.52

Combine like terms: 0.52 + -0.52 = 0.00
0.00 + w = 0.265329983 + -0.52
w = 0.265329983 + -0.52

Combine like terms: 0.265329983 + -0.52 = -0.254670017
w = -0.254670017

Simplifying
w = -0.254670017

Subproblem 2
w + 0.52 = -0.265329983

Simplifying
w + 0.52 = -0.265329983

Reorder the terms:
0.52 + w = -0.265329983

Solving
0.52 + w = -0.265329983

Solving for variable 'w'.

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

Add '-0.52' to each side of the equation.
0.52 + -0.52 + w = -0.265329983 + -0.52

Combine like terms: 0.52 + -0.52 = 0.00
0.00 + w = -0.265329983 + -0.52
w = -0.265329983 + -0.52

Combine like terms: -0.265329983 + -0.52 = -0.785329983
w = -0.785329983

Simplifying
w = -0.785329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.254670017, -0.785329983}