2+w(w-5)=

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

Simplifying
2 + w(w + -5) = 0

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

Solving
2 + -5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = -2 + 6.25

Reorder the terms:
6.25 + -5w + w2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + -5w + w2 = 4.25

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(w + -2.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
w + -2.5 = 2.061552813

Simplifying
w + -2.5 = 2.061552813

Reorder the terms:
-2.5 + w = 2.061552813

Solving
-2.5 + w = 2.061552813

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = 2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = 2.061552813 + 2.5
w = 2.061552813 + 2.5

Combine like terms: 2.061552813 + 2.5 = 4.561552813
w = 4.561552813

Simplifying
w = 4.561552813

Subproblem 2
w + -2.5 = -2.061552813

Simplifying
w + -2.5 = -2.061552813

Reorder the terms:
-2.5 + w = -2.061552813

Solving
-2.5 + w = -2.061552813

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = -2.061552813 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = -2.061552813 + 2.5
w = -2.061552813 + 2.5

Combine like terms: -2.061552813 + 2.5 = 0.438447187
w = 0.438447187

Simplifying
w = 0.438447187

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.561552813, 0.438447187}