x^2-74x+77=0

Solution for x^2-74x+77=0 equation:

Simplifying
x2 + -74x + 77 = 0

Reorder the terms:
77 + -74x + x2 = 0

Solving
77 + -74x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-77' to each side of the equation.
77 + -74x + -77 + x2 = 0 + -77

Reorder the terms:
77 + -77 + -74x + x2 = 0 + -77

Combine like terms: 77 + -77 = 0
0 + -74x + x2 = 0 + -77
-74x + x2 = 0 + -77

Combine like terms: 0 + -77 = -77
-74x + x2 = -77

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 = -77 + 1369

Reorder the terms:
1369 + -74x + x2 = -77 + 1369

Combine like terms: -77 + 1369 = 1292
1369 + -74x + x2 = 1292

Factor a perfect square on the left side:
(x + -37)(x + -37) = 1292

Calculate the square root of the right side: 35.944401511

Break this problem into two subproblems by setting 
(x + -37) equal to 35.944401511 and -35.944401511.

Subproblem 1
x + -37 = 35.944401511

Simplifying
x + -37 = 35.944401511

Reorder the terms:
-37 + x = 35.944401511

Solving
-37 + x = 35.944401511

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 = 35.944401511 + 37

Combine like terms: -37 + 37 = 0
0 + x = 35.944401511 + 37
x = 35.944401511 + 37

Combine like terms: 35.944401511 + 37 = 72.944401511
x = 72.944401511

Simplifying
x = 72.944401511

Subproblem 2
x + -37 = -35.944401511

Simplifying
x + -37 = -35.944401511

Reorder the terms:
-37 + x = -35.944401511

Solving
-37 + x = -35.944401511

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 = -35.944401511 + 37

Combine like terms: -37 + 37 = 0
0 + x = -35.944401511 + 37
x = -35.944401511 + 37

Combine like terms: -35.944401511 + 37 = 1.055598489
x = 1.055598489

Simplifying
x = 1.055598489

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {72.944401511, 1.055598489}