x(x+1)=4

Solution for x(x+1)=4 equation:

Simplifying
x(x + 1) = 4

Reorder the terms:
x(1 + x) = 4
(1 * x + x * x) = 4
(1x + x2) = 4

Solving
1x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1x + x2 = 0 + 4
1x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1x + x2 = 4

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 = 4 + 0.25

Reorder the terms:
0.25 + x + x2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + x + x2 = 4.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
x + 0.5 = 2.061552813

Simplifying
x + 0.5 = 2.061552813

Reorder the terms:
0.5 + x = 2.061552813

Solving
0.5 + x = 2.061552813

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 = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.061552813 + -0.5
x = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
x = 1.561552813

Simplifying
x = 1.561552813

Subproblem 2
x + 0.5 = -2.061552813

Simplifying
x + 0.5 = -2.061552813

Reorder the terms:
0.5 + x = -2.061552813

Solving
0.5 + x = -2.061552813

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 = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.061552813 + -0.5
x = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
x = -2.561552813

Simplifying
x = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.561552813, -2.561552813}