0=x^2-66x+1089

Solution for 0=x^2-66x+1089 equation:

Simplifying
0 = x2 + -66x + 1089

Reorder the terms:
0 = 1089 + -66x + x2

Solving
0 = 1089 + -66x + x2

Solving for variable 'x'.

Combine like terms: 0 + -1089 = -1089
-1089 + 66x + -1x2 = 1089 + -66x + x2 + -1089 + 66x + -1x2

Reorder the terms:
-1089 + 66x + -1x2 = 1089 + -1089 + -66x + 66x + x2 + -1x2

Combine like terms: 1089 + -1089 = 0
-1089 + 66x + -1x2 = 0 + -66x + 66x + x2 + -1x2
-1089 + 66x + -1x2 = -66x + 66x + x2 + -1x2

Combine like terms: -66x + 66x = 0
-1089 + 66x + -1x2 = 0 + x2 + -1x2
-1089 + 66x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1089 + 66x + -1x2 = 0

Factor a trinomial.
(-33 + x)(33 + -1x) = 0

Subproblem 1
Set the factor '(-33 + x)' equal to zero and attempt to solve:

Simplifying
-33 + x = 0

Solving
-33 + x = 0

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

Add '33' to each side of the equation.
-33 + 33 + x = 0 + 33

Combine like terms: -33 + 33 = 0
0 + x = 0 + 33
x = 0 + 33

Combine like terms: 0 + 33 = 33
x = 33

Simplifying
x = 33
Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve:

Simplifying
33 + -1x = 0

Solving
33 + -1x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -1x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -1x = 0 + -33
-1x = 0 + -33

Combine like terms: 0 + -33 = -33
-1x = -33

Divide each side by '-1'.
x = 33

Simplifying
x = 33
Solution
x = {33, 33}