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 = 3375
3600 + -120x + x2 = 3375

Factor a perfect square on the left side:
(x + -60)(x + -60) = 3375

Calculate the square root of the right side: 58.094750193

Break this problem into two subproblems by setting 
(x + -60) equal to 58.094750193 and -58.094750193.


Subproblem 1
x + -60 = 58.094750193

Simplifying
x + -60 = 58.094750193

Reorder the terms:
-60 + x = 58.094750193

Solving
-60 + x = 58.094750193

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 = 58.094750193 + 60

Combine like terms: -60 + 60 = 0
0 + x = 58.094750193 + 60
x = 58.094750193 + 60

Combine like terms: 58.094750193 + 60 = 118.094750193
x = 118.094750193

Simplifying
x = 118.094750193


Subproblem 2
x + -60 = -58.094750193

Simplifying
x + -60 = -58.094750193

Reorder the terms:
-60 + x = -58.094750193

Solving
-60 + x = -58.094750193

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 = -58.094750193 + 60

Combine like terms: -60 + 60 = 0
0 + x = -58.094750193 + 60
x = -58.094750193 + 60

Combine like terms: -58.094750193 + 60 = 1.905249807
x = 1.905249807

Simplifying
x = 1.905249807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {118.094750193, 1.905249807}

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