x^2+x=5.8

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Solution for x^2+x=5.8 equation: 


Simplifying
x2 + x = 5.8

Reorder the terms:
x + x2 = 5.8

Solving
x + x2 = 5.8

Solving for variable 'x'.

Reorder the terms:
-5.8 + x + x2 = 5.8 + -5.8

Combine like terms: 5.8 + -5.8 = 0.0
-5.8 + x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '5.8' to each side of the equation.
-5.8 + x + 5.8 + x2 = 0.0 + 5.8

Reorder the terms:
-5.8 + 5.8 + x + x2 = 0.0 + 5.8

Combine like terms: -5.8 + 5.8 = 0.0
0.0 + x + x2 = 0.0 + 5.8
x + x2 = 0.0 + 5.8

Combine like terms: 0.0 + 5.8 = 5.8
x + x2 = 5.8

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 = 5.8 + 0.25

Reorder the terms:
0.25 + x + x2 = 5.8 + 0.25

Combine like terms: 5.8 + 0.25 = 6.05
0.25 + x + x2 = 6.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6.05

Calculate the square root of the right side: 2.459674775

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.459674775 and -2.459674775.


Subproblem 1
x + 0.5 = 2.459674775

Simplifying
x + 0.5 = 2.459674775

Reorder the terms:
0.5 + x = 2.459674775

Solving
0.5 + x = 2.459674775

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 = 2.459674775 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.459674775 + -0.5
x = 2.459674775 + -0.5

Combine like terms: 2.459674775 + -0.5 = 1.959674775
x = 1.959674775

Simplifying
x = 1.959674775


Subproblem 2
x + 0.5 = -2.459674775

Simplifying
x + 0.5 = -2.459674775

Reorder the terms:
0.5 + x = -2.459674775

Solving
0.5 + x = -2.459674775

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 = -2.459674775 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.459674775 + -0.5
x = -2.459674775 + -0.5

Combine like terms: -2.459674775 + -0.5 = -2.959674775
x = -2.959674775

Simplifying
x = -2.959674775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.959674775, -2.959674775}

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