x^2+20x+59=0

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Solution for x^2+20x+59=0 equation: 


Simplifying
x2 + 20x + 59 = 0

Reorder the terms:
59 + 20x + x2 = 0

Solving
59 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-59' to each side of the equation.
59 + 20x + -59 + x2 = 0 + -59

Reorder the terms:
59 + -59 + 20x + x2 = 0 + -59

Combine like terms: 59 + -59 = 0
0 + 20x + x2 = 0 + -59
20x + x2 = 0 + -59

Combine like terms: 0 + -59 = -59
20x + x2 = -59

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -59 + 100

Reorder the terms:
100 + 20x + x2 = -59 + 100

Combine like terms: -59 + 100 = 41
100 + 20x + x2 = 41

Factor a perfect square on the left side:
(x + 10)(x + 10) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 10) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 10 = 6.403124237

Simplifying
x + 10 = 6.403124237

Reorder the terms:
10 + x = 6.403124237

Solving
10 + x = 6.403124237

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 6.403124237 + -10

Combine like terms: 10 + -10 = 0
0 + x = 6.403124237 + -10
x = 6.403124237 + -10

Combine like terms: 6.403124237 + -10 = -3.596875763
x = -3.596875763

Simplifying
x = -3.596875763


Subproblem 2
x + 10 = -6.403124237

Simplifying
x + 10 = -6.403124237

Reorder the terms:
10 + x = -6.403124237

Solving
10 + x = -6.403124237

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -6.403124237 + -10

Combine like terms: 10 + -10 = 0
0 + x = -6.403124237 + -10
x = -6.403124237 + -10

Combine like terms: -6.403124237 + -10 = -16.403124237
x = -16.403124237

Simplifying
x = -16.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.596875763, -16.403124237}

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