x(x+1)=146

Solution for x(x+1)=146 equation:

Simplifying
x(x + 1) = 146

Reorder the terms:
x(1 + x) = 146
(1 * x + x * x) = 146
(1x + x2) = 146

Solving
1x + x2 = 146

Solving for variable 'x'.

Reorder the terms:
-146 + 1x + x2 = 146 + -146

Combine like terms: 146 + -146 = 0
-146 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + 1x + 146 + x2 = 0 + 146

Reorder the terms:
-146 + 146 + 1x + x2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + 1x + x2 = 0 + 146
1x + x2 = 0 + 146

Combine like terms: 0 + 146 = 146
1x + x2 = 146

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 = 146 + 0.25

Reorder the terms:
0.25 + x + x2 = 146 + 0.25

Combine like terms: 146 + 0.25 = 146.25
0.25 + x + x2 = 146.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 0.5) equal to 12.093386622 and -12.093386622.

Subproblem 1
x + 0.5 = 12.093386622

Simplifying
x + 0.5 = 12.093386622

Reorder the terms:
0.5 + x = 12.093386622

Solving
0.5 + x = 12.093386622

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 = 12.093386622 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 12.093386622 + -0.5
x = 12.093386622 + -0.5

Combine like terms: 12.093386622 + -0.5 = 11.593386622
x = 11.593386622

Simplifying
x = 11.593386622

Subproblem 2
x + 0.5 = -12.093386622

Simplifying
x + 0.5 = -12.093386622

Reorder the terms:
0.5 + x = -12.093386622

Solving
0.5 + x = -12.093386622

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 = -12.093386622 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -12.093386622 + -0.5
x = -12.093386622 + -0.5

Combine like terms: -12.093386622 + -0.5 = -12.593386622
x = -12.593386622

Simplifying
x = -12.593386622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.593386622, -12.593386622}