2x^2-74x+12=0

Solution for 2x^2-74x+12=0 equation:

Simplifying
2x2 + -74x + 12 = 0

Reorder the terms:
12 + -74x + 2x2 = 0

Solving
12 + -74x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -37x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -37x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -37x + x2 = 0

Solving
6 + -37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -37x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -37x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -37x + x2 = 0 + -6
-37x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-37x + x2 = -6

The x term is -37x.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37x + 342.25 + x2 = -6 + 342.25

Reorder the terms:
342.25 + -37x + x2 = -6 + 342.25

Combine like terms: -6 + 342.25 = 336.25
342.25 + -37x + x2 = 336.25

Factor a perfect square on the left side:
(x + -18.5)(x + -18.5) = 336.25

Calculate the square root of the right side: 18.337120821

Break this problem into two subproblems by setting 
(x + -18.5) equal to 18.337120821 and -18.337120821.

Subproblem 1
x + -18.5 = 18.337120821

Simplifying
x + -18.5 = 18.337120821

Reorder the terms:
-18.5 + x = 18.337120821

Solving
-18.5 + x = 18.337120821

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = 18.337120821 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = 18.337120821 + 18.5
x = 18.337120821 + 18.5

Combine like terms: 18.337120821 + 18.5 = 36.837120821
x = 36.837120821

Simplifying
x = 36.837120821

Subproblem 2
x + -18.5 = -18.337120821

Simplifying
x + -18.5 = -18.337120821

Reorder the terms:
-18.5 + x = -18.337120821

Solving
-18.5 + x = -18.337120821

Solving for variable 'x'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + x = -18.337120821 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + x = -18.337120821 + 18.5
x = -18.337120821 + 18.5

Combine like terms: -18.337120821 + 18.5 = 0.162879179
x = 0.162879179

Simplifying
x = 0.162879179

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.837120821, 0.162879179}
Solution
x = {36.837120821, 0.162879179}