x(x+1)=300

Solution for x(x+1)=300 equation:

Simplifying
x(x + 1) = 300

Reorder the terms:
x(1 + x) = 300
(1 * x + x * x) = 300
(1x + x2) = 300

Solving
1x + x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 1x + x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 1x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 1x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 1x + x2 = 0 + 300
1x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
1x + x2 = 300

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 300 + 0.25

Reorder the terms:
0.25 + x + x2 = 300 + 0.25

Combine like terms: 300 + 0.25 = 300.25
0.25 + x + x2 = 300.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 300.25

Calculate the square root of the right side: 17.327723451

Break this problem into two subproblems by setting 
(x + 0.5) equal to 17.327723451 and -17.327723451.

Subproblem 1
x + 0.5 = 17.327723451

Simplifying
x + 0.5 = 17.327723451

Reorder the terms:
0.5 + x = 17.327723451

Solving
0.5 + x = 17.327723451

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 17.327723451 + -0.5
x = 17.327723451 + -0.5

Combine like terms: 17.327723451 + -0.5 = 16.827723451
x = 16.827723451

Simplifying
x = 16.827723451

Subproblem 2
x + 0.5 = -17.327723451

Simplifying
x + 0.5 = -17.327723451

Reorder the terms:
0.5 + x = -17.327723451

Solving
0.5 + x = -17.327723451

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -17.327723451 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -17.327723451 + -0.5
x = -17.327723451 + -0.5

Combine like terms: -17.327723451 + -0.5 = -17.827723451
x = -17.827723451

Simplifying
x = -17.827723451

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.827723451, -17.827723451}