x^2+x+1=3.64

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Solution for x^2+x+1=3.64 equation:


Simplifying
x2 + x + 1 = 3.64

Reorder the terms:
1 + x + x2 = 3.64

Solving
1 + x + x2 = 3.64

Solving for variable 'x'.

Reorder the terms:
1 + -3.64 + x + x2 = 3.64 + -3.64

Combine like terms: 1 + -3.64 = -2.64
-2.64 + x + x2 = 3.64 + -3.64

Combine like terms: 3.64 + -3.64 = 0.00
-2.64 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.64' to each side of the equation.
-2.64 + x + 2.64 + x2 = 0.00 + 2.64

Reorder the terms:
-2.64 + 2.64 + x + x2 = 0.00 + 2.64

Combine like terms: -2.64 + 2.64 = 0.00
0.00 + x + x2 = 0.00 + 2.64
x + x2 = 0.00 + 2.64

Combine like terms: 0.00 + 2.64 = 2.64
x + x2 = 2.64

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 = 2.64 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.64 + 0.25

Combine like terms: 2.64 + 0.25 = 2.89
0.25 + x + x2 = 2.89

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.89

Calculate the square root of the right side: 1.7

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.7 and -1.7.


Subproblem 1
x + 0.5 = 1.7

Simplifying
x + 0.5 = 1.7

Reorder the terms:
0.5 + x = 1.7

Solving
0.5 + x = 1.7

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 = 1.7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.7 + -0.5
x = 1.7 + -0.5

Combine like terms: 1.7 + -0.5 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + 0.5 = -1.7

Simplifying
x + 0.5 = -1.7

Reorder the terms:
0.5 + x = -1.7

Solving
0.5 + x = -1.7

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 = -1.7 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.7 + -0.5
x = -1.7 + -0.5

Combine like terms: -1.7 + -0.5 = -2.2
x = -2.2

Simplifying
x = -2.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, -2.2}

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