2w^2-4w-144=0

Solution for 2w^2-4w-144=0 equation:

Simplifying
2w2 + -4w + -144 = 0

Reorder the terms:
-144 + -4w + 2w2 = 0

Solving
-144 + -4w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -2w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-72 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-72 + -2w + w2 = 0

Solving
-72 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -2w + 72 + w2 = 0 + 72

Reorder the terms:
-72 + 72 + -2w + w2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -2w + w2 = 0 + 72
-2w + w2 = 0 + 72

Combine like terms: 0 + 72 = 72
-2w + w2 = 72

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 = 72 + 1

Reorder the terms:
1 + -2w + w2 = 72 + 1

Combine like terms: 72 + 1 = 73
1 + -2w + w2 = 73

Factor a perfect square on the left side:
(w + -1)(w + -1) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(w + -1) equal to 8.544003745 and -8.544003745.

Subproblem 1
w + -1 = 8.544003745

Simplifying
w + -1 = 8.544003745

Reorder the terms:
-1 + w = 8.544003745

Solving
-1 + w = 8.544003745

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 = 8.544003745 + 1

Combine like terms: -1 + 1 = 0
0 + w = 8.544003745 + 1
w = 8.544003745 + 1

Combine like terms: 8.544003745 + 1 = 9.544003745
w = 9.544003745

Simplifying
w = 9.544003745

Subproblem 2
w + -1 = -8.544003745

Simplifying
w + -1 = -8.544003745

Reorder the terms:
-1 + w = -8.544003745

Solving
-1 + w = -8.544003745

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 = -8.544003745 + 1

Combine like terms: -1 + 1 = 0
0 + w = -8.544003745 + 1
w = -8.544003745 + 1

Combine like terms: -8.544003745 + 1 = -7.544003745
w = -7.544003745

Simplifying
w = -7.544003745

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {9.544003745, -7.544003745}
Solution
w = {9.544003745, -7.544003745}