x^2+x=2.75

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Solution for x^2+x=2.75 equation: 


Simplifying
x2 + x = 2.75

Reorder the terms:
x + x2 = 2.75

Solving
x + x2 = 2.75

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + x + 2.75 + x2 = 0.00 + 2.75

Reorder the terms:
-2.75 + 2.75 + x + x2 = 0.00 + 2.75

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

Combine like terms: 0.00 + 2.75 = 2.75
x + x2 = 2.75

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.
x + 0.25 + x2 = 2.75 + 0.25

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

Combine like terms: 2.75 + 0.25 = 3
0.25 + x + 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 = 1.232050808
x = 1.232050808

Simplifying
x = 1.232050808


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 = -2.232050808
x = -2.232050808

Simplifying
x = -2.232050808


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

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