x^2+20x-587=0

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Solution for x^2+20x-587=0 equation: 


Simplifying
x2 + 20x + -587 = 0

Reorder the terms:
-587 + 20x + x2 = 0

Solving
-587 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '587' to each side of the equation.
-587 + 20x + 587 + x2 = 0 + 587

Reorder the terms:
-587 + 587 + 20x + x2 = 0 + 587

Combine like terms: -587 + 587 = 0
0 + 20x + x2 = 0 + 587
20x + x2 = 0 + 587

Combine like terms: 0 + 587 = 587
20x + x2 = 587

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 = 587 + 100

Reorder the terms:
100 + 20x + x2 = 587 + 100

Combine like terms: 587 + 100 = 687
100 + 20x + x2 = 687

Factor a perfect square on the left side:
(x + 10)(x + 10) = 687

Calculate the square root of the right side: 26.210684844

Break this problem into two subproblems by setting 
(x + 10) equal to 26.210684844 and -26.210684844.


Subproblem 1
x + 10 = 26.210684844

Simplifying
x + 10 = 26.210684844

Reorder the terms:
10 + x = 26.210684844

Solving
10 + x = 26.210684844

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 = 26.210684844 + -10

Combine like terms: 10 + -10 = 0
0 + x = 26.210684844 + -10
x = 26.210684844 + -10

Combine like terms: 26.210684844 + -10 = 16.210684844
x = 16.210684844

Simplifying
x = 16.210684844


Subproblem 2
x + 10 = -26.210684844

Simplifying
x + 10 = -26.210684844

Reorder the terms:
10 + x = -26.210684844

Solving
10 + x = -26.210684844

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 = -26.210684844 + -10

Combine like terms: 10 + -10 = 0
0 + x = -26.210684844 + -10
x = -26.210684844 + -10

Combine like terms: -26.210684844 + -10 = -36.210684844
x = -36.210684844

Simplifying
x = -36.210684844


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.210684844, -36.210684844}

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