X^2-X-2.81=0

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Solution for X^2-X-2.81=0 equation: 


Simplifying
X2 + -1X + -2.81 = 0

Reorder the terms:
-2.81 + -1X + X2 = 0

Solving
-2.81 + -1X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '2.81' to each side of the equation.
-2.81 + -1X + 2.81 + X2 = 0 + 2.81

Reorder the terms:
-2.81 + 2.81 + -1X + X2 = 0 + 2.81

Combine like terms: -2.81 + 2.81 = 0.00
0.00 + -1X + X2 = 0 + 2.81
-1X + X2 = 0 + 2.81

Combine like terms: 0 + 2.81 = 2.81
-1X + X2 = 2.81

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 = 2.81 + 0.25

Reorder the terms:
0.25 + -1X + X2 = 2.81 + 0.25

Combine like terms: 2.81 + 0.25 = 3.06
0.25 + -1X + X2 = 3.06

Factor a perfect square on the left side:
(X + -0.5)(X + -0.5) = 3.06

Calculate the square root of the right side: 1.749285568

Break this problem into two subproblems by setting 
(X + -0.5) equal to 1.749285568 and -1.749285568.


Subproblem 1
X + -0.5 = 1.749285568

Simplifying
X + -0.5 = 1.749285568

Reorder the terms:
-0.5 + X = 1.749285568

Solving
-0.5 + X = 1.749285568

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 = 1.749285568 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = 1.749285568 + 0.5
X = 1.749285568 + 0.5

Combine like terms: 1.749285568 + 0.5 = 2.249285568
X = 2.249285568

Simplifying
X = 2.249285568


Subproblem 2
X + -0.5 = -1.749285568

Simplifying
X + -0.5 = -1.749285568

Reorder the terms:
-0.5 + X = -1.749285568

Solving
-0.5 + X = -1.749285568

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 = -1.749285568 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + X = -1.749285568 + 0.5
X = -1.749285568 + 0.5

Combine like terms: -1.749285568 + 0.5 = -1.249285568
X = -1.249285568

Simplifying
X = -1.249285568


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.249285568, -1.249285568}

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