x^2-74x+120=0

Solution for x^2-74x+120=0 equation:

Simplifying
x2 + -74x + 120 = 0

Reorder the terms:
120 + -74x + x2 = 0

Solving
120 + -74x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -74x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -74x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -74x + x2 = 0 + -120
-74x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-74x + x2 = -120

The x term is -74x.  Take half its coefficient (-37).
Square it (1369) and add it to both sides.

Add '1369' to each side of the equation.
-74x + 1369 + x2 = -120 + 1369

Reorder the terms:
1369 + -74x + x2 = -120 + 1369

Combine like terms: -120 + 1369 = 1249
1369 + -74x + x2 = 1249

Factor a perfect square on the left side:
(x + -37)(x + -37) = 1249

Calculate the square root of the right side: 35.341194094

Break this problem into two subproblems by setting 
(x + -37) equal to 35.341194094 and -35.341194094.

Subproblem 1
x + -37 = 35.341194094

Simplifying
x + -37 = 35.341194094

Reorder the terms:
-37 + x = 35.341194094

Solving
-37 + x = 35.341194094

Solving for variable 'x'.

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

Add '37' to each side of the equation.
-37 + 37 + x = 35.341194094 + 37

Combine like terms: -37 + 37 = 0
0 + x = 35.341194094 + 37
x = 35.341194094 + 37

Combine like terms: 35.341194094 + 37 = 72.341194094
x = 72.341194094

Simplifying
x = 72.341194094

Subproblem 2
x + -37 = -35.341194094

Simplifying
x + -37 = -35.341194094

Reorder the terms:
-37 + x = -35.341194094

Solving
-37 + x = -35.341194094

Solving for variable 'x'.

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

Add '37' to each side of the equation.
-37 + 37 + x = -35.341194094 + 37

Combine like terms: -37 + 37 = 0
0 + x = -35.341194094 + 37
x = -35.341194094 + 37

Combine like terms: -35.341194094 + 37 = 1.658805906
x = 1.658805906

Simplifying
x = 1.658805906

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {72.341194094, 1.658805906}