x^2+x-2=2.71828

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Solution for x^2+x-2=2.71828 equation:


Simplifying
x2 + x + -2 = 2.71828

Reorder the terms:
-2 + x + x2 = 2.71828

Solving
-2 + x + x2 = 2.71828

Solving for variable 'x'.

Reorder the terms:
-2 + -2.71828 + x + x2 = 2.71828 + -2.71828

Combine like terms: -2 + -2.71828 = -4.71828
-4.71828 + x + x2 = 2.71828 + -2.71828

Combine like terms: 2.71828 + -2.71828 = 0.00000
-4.71828 + x + x2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '4.71828' to each side of the equation.
-4.71828 + x + 4.71828 + x2 = 0.00000 + 4.71828

Reorder the terms:
-4.71828 + 4.71828 + x + x2 = 0.00000 + 4.71828

Combine like terms: -4.71828 + 4.71828 = 0.00000
0.00000 + x + x2 = 0.00000 + 4.71828
x + x2 = 0.00000 + 4.71828

Combine like terms: 0.00000 + 4.71828 = 4.71828
x + x2 = 4.71828

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 = 4.71828 + 0.25

Reorder the terms:
0.25 + x + x2 = 4.71828 + 0.25

Combine like terms: 4.71828 + 0.25 = 4.96828
0.25 + x + x2 = 4.96828

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.96828

Calculate the square root of the right side: 2.228963885

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.228963885 and -2.228963885.


Subproblem 1
x + 0.5 = 2.228963885

Simplifying
x + 0.5 = 2.228963885

Reorder the terms:
0.5 + x = 2.228963885

Solving
0.5 + x = 2.228963885

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 = 2.228963885 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.228963885 + -0.5
x = 2.228963885 + -0.5

Combine like terms: 2.228963885 + -0.5 = 1.728963885
x = 1.728963885

Simplifying
x = 1.728963885


Subproblem 2
x + 0.5 = -2.228963885

Simplifying
x + 0.5 = -2.228963885

Reorder the terms:
0.5 + x = -2.228963885

Solving
0.5 + x = -2.228963885

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 = -2.228963885 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.228963885 + -0.5
x = -2.228963885 + -0.5

Combine like terms: -2.228963885 + -0.5 = -2.728963885
x = -2.728963885

Simplifying
x = -2.728963885


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.728963885, -2.728963885}

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