x(x+1)=36.96

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Solution for x(x+1)=36.96 equation: 


Simplifying
x(x + 1) = 36.96

Reorder the terms:
x(1 + x) = 36.96
(1 * x + x * x) = 36.96
(1x + x2) = 36.96

Solving
1x + x2 = 36.96

Solving for variable 'x'.

Reorder the terms:
-36.96 + 1x + x2 = 36.96 + -36.96

Combine like terms: 36.96 + -36.96 = 0.00
-36.96 + 1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '36.96' to each side of the equation.
-36.96 + 1x + 36.96 + x2 = 0.00 + 36.96

Reorder the terms:
-36.96 + 36.96 + 1x + x2 = 0.00 + 36.96

Combine like terms: -36.96 + 36.96 = 0.00
0.00 + 1x + x2 = 0.00 + 36.96
1x + x2 = 0.00 + 36.96

Combine like terms: 0.00 + 36.96 = 36.96
1x + x2 = 36.96

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 = 36.96 + 0.25

Reorder the terms:
0.25 + x + x2 = 36.96 + 0.25

Combine like terms: 36.96 + 0.25 = 37.21
0.25 + x + x2 = 37.21

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 37.21

Calculate the square root of the right side: 6.1

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.1 and -6.1.


Subproblem 1
x + 0.5 = 6.1

Simplifying
x + 0.5 = 6.1

Reorder the terms:
0.5 + x = 6.1

Solving
0.5 + x = 6.1

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 = 6.1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.1 + -0.5
x = 6.1 + -0.5

Combine like terms: 6.1 + -0.5 = 5.6
x = 5.6

Simplifying
x = 5.6


Subproblem 2
x + 0.5 = -6.1

Simplifying
x + 0.5 = -6.1

Reorder the terms:
0.5 + x = -6.1

Solving
0.5 + x = -6.1

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 = -6.1 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.1 + -0.5
x = -6.1 + -0.5

Combine like terms: -6.1 + -0.5 = -6.6
x = -6.6

Simplifying
x = -6.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.6, -6.6}

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