5.88844=x^2+x-6

Solution for 5.88844=x^2+x-6 equation:

Simplifying
5.88844 = x2 + x + -6

Reorder the terms:
5.88844 = -6 + x + x2

Solving
5.88844 = -6 + x + x2

Solving for variable 'x'.

Combine like terms: 5.88844 + 6 = 11.88844
11.88844 + -1x + -1x2 = -6 + x + x2 + 6 + -1x + -1x2

Reorder the terms:
11.88844 + -1x + -1x2 = -6 + 6 + x + -1x + x2 + -1x2

Combine like terms: -6 + 6 = 0
11.88844 + -1x + -1x2 = 0 + x + -1x + x2 + -1x2
11.88844 + -1x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
11.88844 + -1x + -1x2 = 0 + x2 + -1x2
11.88844 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
11.88844 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-11.88844 + x + x2 = 0

Move the constant term to the right:

Add '11.88844' to each side of the equation.
-11.88844 + x + 11.88844 + x2 = 0 + 11.88844

Reorder the terms:
-11.88844 + 11.88844 + x + x2 = 0 + 11.88844

Combine like terms: -11.88844 + 11.88844 = 0.00000
0.00000 + x + x2 = 0 + 11.88844
x + x2 = 0 + 11.88844

Combine like terms: 0 + 11.88844 = 11.88844
x + x2 = 11.88844

The x term is x.  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.
 + 0.25 + x2 = 11.88844 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 11.88844 + 0.25

Combine like terms: 11.88844 + 0.25 = 12.13844
1.25 + x2 = 12.13844

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 12.13844

Calculate the square root of the right side: 3.484026406

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.484026406 and -3.484026406.

Subproblem 1
x + 0.5 = 3.484026406

Simplifying
x + 0.5 = 3.484026406

Reorder the terms:
0.5 + x = 3.484026406

Solving
0.5 + x = 3.484026406

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 = 3.484026406 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.484026406 + -0.5
x = 3.484026406 + -0.5

Combine like terms: 3.484026406 + -0.5 = 2.984026406
x = 2.984026406

Simplifying
x = 2.984026406

Subproblem 2
x + 0.5 = -3.484026406

Simplifying
x + 0.5 = -3.484026406

Reorder the terms:
0.5 + x = -3.484026406

Solving
0.5 + x = -3.484026406

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 = -3.484026406 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.484026406 + -0.5
x = -3.484026406 + -0.5

Combine like terms: -3.484026406 + -0.5 = -3.984026406
x = -3.984026406

Simplifying
x = -3.984026406

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.984026406, -3.984026406}