x^2-120x+900=0

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Solution for x^2-120x+900=0 equation:


Simplifying
x2 + -120x + 900 = 0

Reorder the terms:
900 + -120x + x2 = 0

Solving
900 + -120x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-900' to each side of the equation.
900 + -120x + -900 + x2 = 0 + -900

Reorder the terms:
900 + -900 + -120x + x2 = 0 + -900

Combine like terms: 900 + -900 = 0
0 + -120x + x2 = 0 + -900
-120x + x2 = 0 + -900

Combine like terms: 0 + -900 = -900
-120x + x2 = -900

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 = -900 + 3600

Reorder the terms:
3600 + -120x + x2 = -900 + 3600

Combine like terms: -900 + 3600 = 2700
3600 + -120x + x2 = 2700

Factor a perfect square on the left side:
(x + -60)(x + -60) = 2700

Calculate the square root of the right side: 51.961524227

Break this problem into two subproblems by setting 
(x + -60) equal to 51.961524227 and -51.961524227.

Subproblem 1

x + -60 = 51.961524227 Simplifying x + -60 = 51.961524227 Reorder the terms: -60 + x = 51.961524227 Solving -60 + x = 51.961524227 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 = 51.961524227 + 60 Combine like terms: -60 + 60 = 0 0 + x = 51.961524227 + 60 x = 51.961524227 + 60 Combine like terms: 51.961524227 + 60 = 111.961524227 x = 111.961524227 Simplifying x = 111.961524227

Subproblem 2

x + -60 = -51.961524227 Simplifying x + -60 = -51.961524227 Reorder the terms: -60 + x = -51.961524227 Solving -60 + x = -51.961524227 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 = -51.961524227 + 60 Combine like terms: -60 + 60 = 0 0 + x = -51.961524227 + 60 x = -51.961524227 + 60 Combine like terms: -51.961524227 + 60 = 8.038475773 x = 8.038475773 Simplifying x = 8.038475773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {111.961524227, 8.038475773}

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