x^2+120x-869=0

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Solution for x^2+120x-869=0 equation: 


Simplifying
x2 + 120x + -869 = 0

Reorder the terms:
-869 + 120x + x2 = 0

Solving
-869 + 120x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '869' to each side of the equation.
-869 + 120x + 869 + x2 = 0 + 869

Reorder the terms:
-869 + 869 + 120x + x2 = 0 + 869

Combine like terms: -869 + 869 = 0
0 + 120x + x2 = 0 + 869
120x + x2 = 0 + 869

Combine like terms: 0 + 869 = 869
120x + x2 = 869

The x term is 120x.  Take half its coefficient (60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
120x + 3600 + x2 = 869 + 3600

Reorder the terms:
3600 + 120x + x2 = 869 + 3600

Combine like terms: 869 + 3600 = 4469
3600 + 120x + x2 = 4469

Factor a perfect square on the left side:
(x + 60)(x + 60) = 4469

Calculate the square root of the right side: 66.850579653

Break this problem into two subproblems by setting 
(x + 60) equal to 66.850579653 and -66.850579653.


Subproblem 1
x + 60 = 66.850579653

Simplifying
x + 60 = 66.850579653

Reorder the terms:
60 + x = 66.850579653

Solving
60 + x = 66.850579653

Solving for variable 'x'.

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

Add '-60' to each side of the equation.
60 + -60 + x = 66.850579653 + -60

Combine like terms: 60 + -60 = 0
0 + x = 66.850579653 + -60
x = 66.850579653 + -60

Combine like terms: 66.850579653 + -60 = 6.850579653
x = 6.850579653

Simplifying
x = 6.850579653


Subproblem 2
x + 60 = -66.850579653

Simplifying
x + 60 = -66.850579653

Reorder the terms:
60 + x = -66.850579653

Solving
60 + x = -66.850579653

Solving for variable 'x'.

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

Add '-60' to each side of the equation.
60 + -60 + x = -66.850579653 + -60

Combine like terms: 60 + -60 = 0
0 + x = -66.850579653 + -60
x = -66.850579653 + -60

Combine like terms: -66.850579653 + -60 = -126.850579653
x = -126.850579653

Simplifying
x = -126.850579653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.850579653, -126.850579653}

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