2x^2-28x+40=0

Solution for 2x^2-28x+40=0 equation:

Simplifying
2x2 + -28x + 40 = 0

Reorder the terms:
40 + -28x + 2x2 = 0

Solving
40 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -14x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
20 + -14x + x2 = 0

Solving
20 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -14x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -14x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -14x + x2 = 0 + -20
-14x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-14x + x2 = -20

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -20 + 49

Reorder the terms:
49 + -14x + x2 = -20 + 49

Combine like terms: -20 + 49 = 29
49 + -14x + x2 = 29

Factor a perfect square on the left side:
(x + -7)(x + -7) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -7) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + -7 = 5.385164807

Simplifying
x + -7 = 5.385164807

Reorder the terms:
-7 + x = 5.385164807

Solving
-7 + x = 5.385164807

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.385164807 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.385164807 + 7
x = 5.385164807 + 7

Combine like terms: 5.385164807 + 7 = 12.385164807
x = 12.385164807

Simplifying
x = 12.385164807

Subproblem 2
x + -7 = -5.385164807

Simplifying
x + -7 = -5.385164807

Reorder the terms:
-7 + x = -5.385164807

Solving
-7 + x = -5.385164807

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.385164807 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.385164807 + 7
x = -5.385164807 + 7

Combine like terms: -5.385164807 + 7 = 1.614835193
x = 1.614835193

Simplifying
x = 1.614835193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.385164807, 1.614835193}
Solution
x = {12.385164807, 1.614835193}