x+x^2=12.86

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Solution for x+x^2=12.86 equation:


Simplifying
x + x2 = 12.86

Solving
x + x2 = 12.86

Solving for variable 'x'.

Reorder the terms:
-12.86 + x + x2 = 12.86 + -12.86

Combine like terms: 12.86 + -12.86 = 0.00
-12.86 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '12.86' to each side of the equation.
-12.86 + x + 12.86 + x2 = 0.00 + 12.86

Reorder the terms:
-12.86 + 12.86 + x + x2 = 0.00 + 12.86

Combine like terms: -12.86 + 12.86 = 0.00
0.00 + x + x2 = 0.00 + 12.86
x + x2 = 0.00 + 12.86

Combine like terms: 0.00 + 12.86 = 12.86
x + x2 = 12.86

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 = 12.86 + 0.25

Reorder the terms:
0.25 + x + x2 = 12.86 + 0.25

Combine like terms: 12.86 + 0.25 = 13.11
0.25 + x + x2 = 13.11

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 13.11

Calculate the square root of the right side: 3.620773398

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.620773398 and -3.620773398.


Subproblem 1
x + 0.5 = 3.620773398

Simplifying
x + 0.5 = 3.620773398

Reorder the terms:
0.5 + x = 3.620773398

Solving
0.5 + x = 3.620773398

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 = 3.620773398 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.620773398 + -0.5
x = 3.620773398 + -0.5

Combine like terms: 3.620773398 + -0.5 = 3.120773398
x = 3.120773398

Simplifying
x = 3.120773398


Subproblem 2
x + 0.5 = -3.620773398

Simplifying
x + 0.5 = -3.620773398

Reorder the terms:
0.5 + x = -3.620773398

Solving
0.5 + x = -3.620773398

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 = -3.620773398 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.620773398 + -0.5
x = -3.620773398 + -0.5

Combine like terms: -3.620773398 + -0.5 = -4.120773398
x = -4.120773398

Simplifying
x = -4.120773398


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.120773398, -4.120773398}

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