(2x^2)-40x+144=0

Solution for (2x^2)-40x+144=0 equation:

Simplifying
(2x2) + -40x + 144 = 0

Reorder the terms:
144 + -40x + (2x2) = 0

Solving
144 + -40x + (2x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + -20x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(72 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
72 + -20x + x2 = 0

Solving
72 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -20x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + -20x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -20x + x2 = 0 + -72
-20x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-20x + x2 = -72

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -72 + 100

Reorder the terms:
100 + -20x + x2 = -72 + 100

Combine like terms: -72 + 100 = 28
100 + -20x + x2 = 28

Factor a perfect square on the left side:
(x + -10)(x + -10) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -10) equal to 5.291502622 and -5.291502622.

Subproblem 1
x + -10 = 5.291502622

Simplifying
x + -10 = 5.291502622

Reorder the terms:
-10 + x = 5.291502622

Solving
-10 + x = 5.291502622

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 5.291502622 + 10

Combine like terms: -10 + 10 = 0
0 + x = 5.291502622 + 10
x = 5.291502622 + 10

Combine like terms: 5.291502622 + 10 = 15.291502622
x = 15.291502622

Simplifying
x = 15.291502622

Subproblem 2
x + -10 = -5.291502622

Simplifying
x + -10 = -5.291502622

Reorder the terms:
-10 + x = -5.291502622

Solving
-10 + x = -5.291502622

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -5.291502622 + 10

Combine like terms: -10 + 10 = 0
0 + x = -5.291502622 + 10
x = -5.291502622 + 10

Combine like terms: -5.291502622 + 10 = 4.708497378
x = 4.708497378

Simplifying
x = 4.708497378

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.291502622, 4.708497378}
Solution
x = {15.291502622, 4.708497378}