x^2-x-11.99=0

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Solution for x^2-x-11.99=0 equation: 


Simplifying
x2 + -1x + -11.99 = 0

Reorder the terms:
-11.99 + -1x + x2 = 0

Solving
-11.99 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11.99' to each side of the equation.
-11.99 + -1x + 11.99 + x2 = 0 + 11.99

Reorder the terms:
-11.99 + 11.99 + -1x + x2 = 0 + 11.99

Combine like terms: -11.99 + 11.99 = 0.00
0.00 + -1x + x2 = 0 + 11.99
-1x + x2 = 0 + 11.99

Combine like terms: 0 + 11.99 = 11.99
-1x + x2 = 11.99

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.
-1x + 0.25 + x2 = 11.99 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 11.99 + 0.25

Combine like terms: 11.99 + 0.25 = 12.24
0.25 + -1x + x2 = 12.24

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 12.24

Calculate the square root of the right side: 3.498571137

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.498571137 and -3.498571137.


Subproblem 1
x + -0.5 = 3.498571137

Simplifying
x + -0.5 = 3.498571137

Reorder the terms:
-0.5 + x = 3.498571137

Solving
-0.5 + x = 3.498571137

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 = 3.498571137 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 3.498571137 + 0.5
x = 3.498571137 + 0.5

Combine like terms: 3.498571137 + 0.5 = 3.998571137
x = 3.998571137

Simplifying
x = 3.998571137


Subproblem 2
x + -0.5 = -3.498571137

Simplifying
x + -0.5 = -3.498571137

Reorder the terms:
-0.5 + x = -3.498571137

Solving
-0.5 + x = -3.498571137

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 = -3.498571137 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -3.498571137 + 0.5
x = -3.498571137 + 0.5

Combine like terms: -3.498571137 + 0.5 = -2.998571137
x = -2.998571137

Simplifying
x = -2.998571137


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.998571137, -2.998571137}

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