k^2-14k+33=0

Solution for k^2-14k+33=0 equation:

Simplifying
k2 + -14k + 33 = 0

Reorder the terms:
33 + -14k + k2 = 0

Solving
33 + -14k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + -1k)(11 + -1k) = 0

Subproblem 1
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Subproblem 2
Set the factor '(11 + -1k)' equal to zero and attempt to solve:

Simplifying
11 + -1k = 0

Solving
11 + -1k = 0

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

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

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

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

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

Simplifying
k = 11
Solution
k = {3, 11}