x^2+x=5806.436

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Solution for x^2+x=5806.436 equation:


Simplifying
x2 + x = 5806.436

Reorder the terms:
x + x2 = 5806.436

Solving
x + x2 = 5806.436

Solving for variable 'x'.

Reorder the terms:
-5806.436 + x + x2 = 5806.436 + -5806.436

Combine like terms: 5806.436 + -5806.436 = 0.000
-5806.436 + x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '5806.436' to each side of the equation.
-5806.436 + x + 5806.436 + x2 = 0.000 + 5806.436

Reorder the terms:
-5806.436 + 5806.436 + x + x2 = 0.000 + 5806.436

Combine like terms: -5806.436 + 5806.436 = 0.000
0.000 + x + x2 = 0.000 + 5806.436
x + x2 = 0.000 + 5806.436

Combine like terms: 0.000 + 5806.436 = 5806.436
x + x2 = 5806.436

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 = 5806.436 + 0.25

Reorder the terms:
0.25 + x + x2 = 5806.436 + 0.25

Combine like terms: 5806.436 + 0.25 = 5806.686
0.25 + x + x2 = 5806.686

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5806.686

Calculate the square root of the right side: 76.201614156

Break this problem into two subproblems by setting 
(x + 0.5) equal to 76.201614156 and -76.201614156.


Subproblem 1
x + 0.5 = 76.201614156

Simplifying
x + 0.5 = 76.201614156

Reorder the terms:
0.5 + x = 76.201614156

Solving
0.5 + x = 76.201614156

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 = 76.201614156 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 76.201614156 + -0.5
x = 76.201614156 + -0.5

Combine like terms: 76.201614156 + -0.5 = 75.701614156
x = 75.701614156

Simplifying
x = 75.701614156


Subproblem 2
x + 0.5 = -76.201614156

Simplifying
x + 0.5 = -76.201614156

Reorder the terms:
0.5 + x = -76.201614156

Solving
0.5 + x = -76.201614156

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 = -76.201614156 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -76.201614156 + -0.5
x = -76.201614156 + -0.5

Combine like terms: -76.201614156 + -0.5 = -76.701614156
x = -76.701614156

Simplifying
x = -76.701614156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {75.701614156, -76.701614156}

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