x^2-1200x+3600=0

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Solution for x^2-1200x+3600=0 equation:


Simplifying
x2 + -1200x + 3600 = 0

Reorder the terms:
3600 + -1200x + x2 = 0

Solving
3600 + -1200x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3600' to each side of the equation.
3600 + -1200x + -3600 + x2 = 0 + -3600

Reorder the terms:
3600 + -3600 + -1200x + x2 = 0 + -3600

Combine like terms: 3600 + -3600 = 0
0 + -1200x + x2 = 0 + -3600
-1200x + x2 = 0 + -3600

Combine like terms: 0 + -3600 = -3600
-1200x + x2 = -3600

The x term is -1200x.  Take half its coefficient (-600).
Square it (360000) and add it to both sides.

Add '360000' to each side of the equation.
-1200x + 360000 + x2 = -3600 + 360000

Reorder the terms:
360000 + -1200x + x2 = -3600 + 360000

Combine like terms: -3600 + 360000 = 356400
360000 + -1200x + x2 = 356400

Factor a perfect square on the left side:
(x + -600)(x + -600) = 356400

Calculate the square root of the right side: 596.992462264

Break this problem into two subproblems by setting 
(x + -600) equal to 596.992462264 and -596.992462264.

Subproblem 1

x + -600 = 596.992462264 Simplifying x + -600 = 596.992462264 Reorder the terms: -600 + x = 596.992462264 Solving -600 + x = 596.992462264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = 596.992462264 + 600 Combine like terms: -600 + 600 = 0 0 + x = 596.992462264 + 600 x = 596.992462264 + 600 Combine like terms: 596.992462264 + 600 = 1196.992462264 x = 1196.992462264 Simplifying x = 1196.992462264

Subproblem 2

x + -600 = -596.992462264 Simplifying x + -600 = -596.992462264 Reorder the terms: -600 + x = -596.992462264 Solving -600 + x = -596.992462264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = -596.992462264 + 600 Combine like terms: -600 + 600 = 0 0 + x = -596.992462264 + 600 x = -596.992462264 + 600 Combine like terms: -596.992462264 + 600 = 3.007537736 x = 3.007537736 Simplifying x = 3.007537736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1196.992462264, 3.007537736}

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