x^2-52x+451=0

Solution for x^2-52x+451=0 equation:

Simplifying
x2 + -52x + 451 = 0

Reorder the terms:
451 + -52x + x2 = 0

Solving
451 + -52x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(11 + -1x)(41 + -1x) = 0

Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Subproblem 2
Set the factor '(41 + -1x)' equal to zero and attempt to solve:

Simplifying
41 + -1x = 0

Solving
41 + -1x = 0

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

Add '-41' to each side of the equation.
41 + -41 + -1x = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -1x = 0 + -41
-1x = 0 + -41

Combine like terms: 0 + -41 = -41
-1x = -41

Divide each side by '-1'.
x = 41

Simplifying
x = 41
Solution
x = {11, 41}