x^2-x-2.75=0

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Solution for x^2-x-2.75=0 equation: 


Simplifying
x2 + -1x + -2.75 = 0

Reorder the terms:
-2.75 + -1x + x2 = 0

Solving
-2.75 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -1x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -1x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -1x + x2 = 0 + 2.75
-1x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-1x + x2 = 2.75

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 = 2.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2.75 + 0.25

Combine like terms: 2.75 + 0.25 = 3
0.25 + -1x + x2 = 3

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -0.5 = 1.732050808

Simplifying
x + -0.5 = 1.732050808

Reorder the terms:
-0.5 + x = 1.732050808

Solving
-0.5 + x = 1.732050808

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 = 1.732050808 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.732050808 + 0.5
x = 1.732050808 + 0.5

Combine like terms: 1.732050808 + 0.5 = 2.232050808
x = 2.232050808

Simplifying
x = 2.232050808


Subproblem 2
x + -0.5 = -1.732050808

Simplifying
x + -0.5 = -1.732050808

Reorder the terms:
-0.5 + x = -1.732050808

Solving
-0.5 + x = -1.732050808

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 = -1.732050808 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.732050808 + 0.5
x = -1.732050808 + 0.5

Combine like terms: -1.732050808 + 0.5 = -1.232050808
x = -1.232050808

Simplifying
x = -1.232050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.232050808, -1.232050808}

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