493=x^2+x+31

Solution for 493=x^2+x+31 equation:

Simplifying
493 = x2 + x + 31

Reorder the terms:
493 = 31 + x + x2

Solving
493 = 31 + x + x2

Solving for variable 'x'.

Combine like terms: 493 + -31 = 462
462 + -1x + -1x2 = 31 + x + x2 + -31 + -1x + -1x2

Reorder the terms:
462 + -1x + -1x2 = 31 + -31 + x + -1x + x2 + -1x2

Combine like terms: 31 + -31 = 0
462 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
462 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
462 + -1x + -1x2 = 0 + x2 + -1x2
462 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
462 + -1x + -1x2 = 0

Factor a trinomial.
(21 + -1x)(22 + x) = 0

Subproblem 1
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Subproblem 2
Set the factor '(22 + x)' equal to zero and attempt to solve:

Simplifying
22 + x = 0

Solving
22 + x = 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 + x = 0 + -22

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

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

Simplifying
x = -22
Solution
x = {21, -22}