x^2=21x+22

Solution for x^2=21x+22 equation:

Simplifying
x2 = 21x + 22

Reorder the terms:
x2 = 22 + 21x

Solving
x2 = 22 + 21x

Solving for variable 'x'.

Reorder the terms:
-22 + -21x + x2 = 22 + 21x + -22 + -21x

Reorder the terms:
-22 + -21x + x2 = 22 + -22 + 21x + -21x

Combine like terms: 22 + -22 = 0
-22 + -21x + x2 = 0 + 21x + -21x
-22 + -21x + x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-22 + -21x + x2 = 0

Factor a trinomial.
(-1 + -1x)(22 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-1, 22}