x+(x+500)+x^2=2900

Solution for x+(x+500)+x^2=2900 equation:

Simplifying
x + (x + 500) + x2 = 2900

Reorder the terms:
x + (500 + x) + x2 = 2900

Remove parenthesis around (500 + x)
x + 500 + x + x2 = 2900

Reorder the terms:
500 + x + x + x2 = 2900

Combine like terms: x + x = 2x
500 + 2x + x2 = 2900

Solving
500 + 2x + x2 = 2900

Solving for variable 'x'.

Reorder the terms:
500 + -2900 + 2x + x2 = 2900 + -2900

Combine like terms: 500 + -2900 = -2400
-2400 + 2x + x2 = 2900 + -2900

Combine like terms: 2900 + -2900 = 0
-2400 + 2x + x2 = 0

Factor a trinomial.
(-50 + -1x)(48 + -1x) = 0

Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
Subproblem 2
Set the factor '(48 + -1x)' equal to zero and attempt to solve:

Simplifying
48 + -1x = 0

Solving
48 + -1x = 0

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

Add '-48' to each side of the equation.
48 + -48 + -1x = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -1x = 0 + -48
-1x = 0 + -48

Combine like terms: 0 + -48 = -48
-1x = -48

Divide each side by '-1'.
x = 48

Simplifying
x = 48
Solution
x = {-50, 48}