x^2-120x-225=0

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Solution for x^2-120x-225=0 equation: 


Simplifying
x2 + -120x + -225 = 0

Reorder the terms:
-225 + -120x + x2 = 0

Solving
-225 + -120x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -120x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -120x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -120x + x2 = 0 + 225
-120x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-120x + x2 = 225

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 = 225 + 3600

Reorder the terms:
3600 + -120x + x2 = 225 + 3600

Combine like terms: 225 + 3600 = 3825
3600 + -120x + x2 = 3825

Factor a perfect square on the left side:
(x + -60)(x + -60) = 3825

Calculate the square root of the right side: 61.846584384

Break this problem into two subproblems by setting 
(x + -60) equal to 61.846584384 and -61.846584384.


Subproblem 1
x + -60 = 61.846584384

Simplifying
x + -60 = 61.846584384

Reorder the terms:
-60 + x = 61.846584384

Solving
-60 + x = 61.846584384

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 = 61.846584384 + 60

Combine like terms: -60 + 60 = 0
0 + x = 61.846584384 + 60
x = 61.846584384 + 60

Combine like terms: 61.846584384 + 60 = 121.846584384
x = 121.846584384

Simplifying
x = 121.846584384


Subproblem 2
x + -60 = -61.846584384

Simplifying
x + -60 = -61.846584384

Reorder the terms:
-60 + x = -61.846584384

Solving
-60 + x = -61.846584384

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 = -61.846584384 + 60

Combine like terms: -60 + 60 = 0
0 + x = -61.846584384 + 60
x = -61.846584384 + 60

Combine like terms: -61.846584384 + 60 = -1.846584384
x = -1.846584384

Simplifying
x = -1.846584384


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {121.846584384, -1.846584384}

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