x(x+1)=650

Solution for x(x+1)=650 equation:

Simplifying
x(x + 1) = 650

Reorder the terms:
x(1 + x) = 650
(1 * x + x * x) = 650
(1x + x2) = 650

Solving
1x + x2 = 650

Solving for variable 'x'.

Reorder the terms:
-650 + 1x + x2 = 650 + -650

Combine like terms: 650 + -650 = 0
-650 + 1x + x2 = 0

Factor a trinomial.
(-26 + -1x)(25 + -1x) = 0

Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26
Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {-26, 25}