x^2+x+500=1430

Solution for x^2+x+500=1430 equation:

Simplifying
x2 + x + 500 = 1430

Reorder the terms:
500 + x + x2 = 1430

Solving
500 + x + x2 = 1430

Solving for variable 'x'.

Reorder the terms:
500 + -1430 + x + x2 = 1430 + -1430

Combine like terms: 500 + -1430 = -930
-930 + x + x2 = 1430 + -1430

Combine like terms: 1430 + -1430 = 0
-930 + x + x2 = 0

Factor a trinomial.
(-31 + -1x)(30 + -1x) = 0

Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve:

Simplifying
-31 + -1x = 0

Solving
-31 + -1x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1x = 0 + 31

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

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

Divide each side by '-1'.
x = -31

Simplifying
x = -31
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-31, 30}