2(w^2-2w)=5

Solution for 2(w^2-2w)=5 equation:

Simplifying
2(w2 + -2w) = 5

Reorder the terms:
2(-2w + w2) = 5
(-2w * 2 + w2 * 2) = 5
(-4w + 2w2) = 5

Solving
-4w + 2w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + -4w + 2w2 = 5 + -5

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

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

Divide each side by '2'.
-2.5 + -2w + w2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2w + 2.5 + w2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2w + w2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2w + w2 = 0 + 2.5
-2w + w2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2w + w2 = 2.5

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 = 2.5 + 1

Reorder the terms:
1 + -2w + w2 = 2.5 + 1

Combine like terms: 2.5 + 1 = 3.5
1 + -2w + w2 = 3.5

Factor a perfect square on the left side:
(w + -1)(w + -1) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(w + -1) equal to 1.870828693 and -1.870828693.

Subproblem 1
w + -1 = 1.870828693

Simplifying
w + -1 = 1.870828693

Reorder the terms:
-1 + w = 1.870828693

Solving
-1 + w = 1.870828693

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 = 1.870828693 + 1

Combine like terms: -1 + 1 = 0
0 + w = 1.870828693 + 1
w = 1.870828693 + 1

Combine like terms: 1.870828693 + 1 = 2.870828693
w = 2.870828693

Simplifying
w = 2.870828693

Subproblem 2
w + -1 = -1.870828693

Simplifying
w + -1 = -1.870828693

Reorder the terms:
-1 + w = -1.870828693

Solving
-1 + w = -1.870828693

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 = -1.870828693 + 1

Combine like terms: -1 + 1 = 0
0 + w = -1.870828693 + 1
w = -1.870828693 + 1

Combine like terms: -1.870828693 + 1 = -0.870828693
w = -0.870828693

Simplifying
w = -0.870828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.870828693, -0.870828693}