x^2=14x-33

Solution for x^2=14x-33 equation:

Simplifying
x2 = 14x + -33

Reorder the terms:
x2 = -33 + 14x

Solving
x2 = -33 + 14x

Solving for variable 'x'.

Reorder the terms:
33 + -14x + x2 = -33 + 14x + 33 + -14x

Reorder the terms:
33 + -14x + x2 = -33 + 33 + 14x + -14x

Combine like terms: -33 + 33 = 0
33 + -14x + x2 = 0 + 14x + -14x
33 + -14x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
33 + -14x + x2 = 0

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

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

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

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

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

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, 11}