x^2+x=4.27

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Solution for x^2+x=4.27 equation: 


Simplifying
x2 + x = 4.27

Reorder the terms:
x + x2 = 4.27

Solving
x + x2 = 4.27

Solving for variable 'x'.

Reorder the terms:
-4.27 + x + x2 = 4.27 + -4.27

Combine like terms: 4.27 + -4.27 = 0.00
-4.27 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '4.27' to each side of the equation.
-4.27 + x + 4.27 + x2 = 0.00 + 4.27

Reorder the terms:
-4.27 + 4.27 + x + x2 = 0.00 + 4.27

Combine like terms: -4.27 + 4.27 = 0.00
0.00 + x + x2 = 0.00 + 4.27
x + x2 = 0.00 + 4.27

Combine like terms: 0.00 + 4.27 = 4.27
x + x2 = 4.27

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 = 4.27 + 0.25

Reorder the terms:
0.25 + x + x2 = 4.27 + 0.25

Combine like terms: 4.27 + 0.25 = 4.52
0.25 + x + x2 = 4.52

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4.52

Calculate the square root of the right side: 2.126029163

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.126029163 and -2.126029163.


Subproblem 1
x + 0.5 = 2.126029163

Simplifying
x + 0.5 = 2.126029163

Reorder the terms:
0.5 + x = 2.126029163

Solving
0.5 + x = 2.126029163

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 = 2.126029163 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.126029163 + -0.5
x = 2.126029163 + -0.5

Combine like terms: 2.126029163 + -0.5 = 1.626029163
x = 1.626029163

Simplifying
x = 1.626029163


Subproblem 2
x + 0.5 = -2.126029163

Simplifying
x + 0.5 = -2.126029163

Reorder the terms:
0.5 + x = -2.126029163

Solving
0.5 + x = -2.126029163

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 = -2.126029163 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.126029163 + -0.5
x = -2.126029163 + -0.5

Combine like terms: -2.126029163 + -0.5 = -2.626029163
x = -2.626029163

Simplifying
x = -2.626029163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.626029163, -2.626029163}

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