x^2+258.86x+10.886=0

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Solution for x^2+258.86x+10.886=0 equation: 


Simplifying
x2 + 258.86x + 10.886 = 0

Reorder the terms:
10.886 + 258.86x + x2 = 0

Solving
10.886 + 258.86x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-10.886' to each side of the equation.
10.886 + 258.86x + -10.886 + x2 = 0 + -10.886

Reorder the terms:
10.886 + -10.886 + 258.86x + x2 = 0 + -10.886

Combine like terms: 10.886 + -10.886 = 0.000
0.000 + 258.86x + x2 = 0 + -10.886
258.86x + x2 = 0 + -10.886

Combine like terms: 0 + -10.886 = -10.886
258.86x + x2 = -10.886

The x term is 258.86x.  Take half its coefficient (129.43).
Square it (16752.1249) and add it to both sides.

Add '16752.1249' to each side of the equation.
258.86x + 16752.1249 + x2 = -10.886 + 16752.1249

Reorder the terms:
16752.1249 + 258.86x + x2 = -10.886 + 16752.1249

Combine like terms: -10.886 + 16752.1249 = 16741.2389
16752.1249 + 258.86x + x2 = 16741.2389

Factor a perfect square on the left side:
(x + 129.43)(x + 129.43) = 16741.2389

Calculate the square root of the right side: 129.387939546

Break this problem into two subproblems by setting 
(x + 129.43) equal to 129.387939546 and -129.387939546.


Subproblem 1
x + 129.43 = 129.387939546

Simplifying
x + 129.43 = 129.387939546

Reorder the terms:
129.43 + x = 129.387939546

Solving
129.43 + x = 129.387939546

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-129.43' to each side of the equation.
129.43 + -129.43 + x = 129.387939546 + -129.43

Combine like terms: 129.43 + -129.43 = 0.00
0.00 + x = 129.387939546 + -129.43
x = 129.387939546 + -129.43

Combine like terms: 129.387939546 + -129.43 = -0.042060454
x = -0.042060454

Simplifying
x = -0.042060454


Subproblem 2
x + 129.43 = -129.387939546

Simplifying
x + 129.43 = -129.387939546

Reorder the terms:
129.43 + x = -129.387939546

Solving
129.43 + x = -129.387939546

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-129.43' to each side of the equation.
129.43 + -129.43 + x = -129.387939546 + -129.43

Combine like terms: 129.43 + -129.43 = 0.00
0.00 + x = -129.387939546 + -129.43
x = -129.387939546 + -129.43

Combine like terms: -129.387939546 + -129.43 = -258.817939546
x = -258.817939546

Simplifying
x = -258.817939546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.042060454, -258.817939546}

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