x^2-360x-210=0

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Solution for x^2-360x-210=0 equation: 


Simplifying
x2 + -360x + -210 = 0

Reorder the terms:
-210 + -360x + x2 = 0

Solving
-210 + -360x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + -360x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + -360x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + -360x + x2 = 0 + 210
-360x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
-360x + x2 = 210

The x term is -360x.  Take half its coefficient (-180).
Square it (32400) and add it to both sides.

Add '32400' to each side of the equation.
-360x + 32400 + x2 = 210 + 32400

Reorder the terms:
32400 + -360x + x2 = 210 + 32400

Combine like terms: 210 + 32400 = 32610
32400 + -360x + x2 = 32610

Factor a perfect square on the left side:
(x + -180)(x + -180) = 32610

Calculate the square root of the right side: 180.582391168

Break this problem into two subproblems by setting 
(x + -180) equal to 180.582391168 and -180.582391168.


Subproblem 1
x + -180 = 180.582391168

Simplifying
x + -180 = 180.582391168

Reorder the terms:
-180 + x = 180.582391168

Solving
-180 + x = 180.582391168

Solving for variable 'x'.

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

Add '180' to each side of the equation.
-180 + 180 + x = 180.582391168 + 180

Combine like terms: -180 + 180 = 0
0 + x = 180.582391168 + 180
x = 180.582391168 + 180

Combine like terms: 180.582391168 + 180 = 360.582391168
x = 360.582391168

Simplifying
x = 360.582391168


Subproblem 2
x + -180 = -180.582391168

Simplifying
x + -180 = -180.582391168

Reorder the terms:
-180 + x = -180.582391168

Solving
-180 + x = -180.582391168

Solving for variable 'x'.

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

Add '180' to each side of the equation.
-180 + 180 + x = -180.582391168 + 180

Combine like terms: -180 + 180 = 0
0 + x = -180.582391168 + 180
x = -180.582391168 + 180

Combine like terms: -180.582391168 + 180 = -0.582391168
x = -0.582391168

Simplifying
x = -0.582391168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {360.582391168, -0.582391168}

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