x^2-1734x+14199=0

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Solution for x^2-1734x+14199=0 equation:


Simplifying
x2 + -1734x + 14199 = 0

Reorder the terms:
14199 + -1734x + x2 = 0

Solving
14199 + -1734x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-14199' to each side of the equation.
14199 + -1734x + -14199 + x2 = 0 + -14199

Reorder the terms:
14199 + -14199 + -1734x + x2 = 0 + -14199

Combine like terms: 14199 + -14199 = 0
0 + -1734x + x2 = 0 + -14199
-1734x + x2 = 0 + -14199

Combine like terms: 0 + -14199 = -14199
-1734x + x2 = -14199

The x term is -1734x.  Take half its coefficient (-867).
Square it (751689) and add it to both sides.

Add '751689' to each side of the equation.
-1734x + 751689 + x2 = -14199 + 751689

Reorder the terms:
751689 + -1734x + x2 = -14199 + 751689

Combine like terms: -14199 + 751689 = 737490
751689 + -1734x + x2 = 737490

Factor a perfect square on the left side:
(x + -867)(x + -867) = 737490

Calculate the square root of the right side: 858.772379621

Break this problem into two subproblems by setting 
(x + -867) equal to 858.772379621 and -858.772379621.

Subproblem 1

x + -867 = 858.772379621 Simplifying x + -867 = 858.772379621 Reorder the terms: -867 + x = 858.772379621 Solving -867 + x = 858.772379621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '867' to each side of the equation. -867 + 867 + x = 858.772379621 + 867 Combine like terms: -867 + 867 = 0 0 + x = 858.772379621 + 867 x = 858.772379621 + 867 Combine like terms: 858.772379621 + 867 = 1725.772379621 x = 1725.772379621 Simplifying x = 1725.772379621

Subproblem 2

x + -867 = -858.772379621 Simplifying x + -867 = -858.772379621 Reorder the terms: -867 + x = -858.772379621 Solving -867 + x = -858.772379621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '867' to each side of the equation. -867 + 867 + x = -858.772379621 + 867 Combine like terms: -867 + 867 = 0 0 + x = -858.772379621 + 867 x = -858.772379621 + 867 Combine like terms: -858.772379621 + 867 = 8.227620379 x = 8.227620379 Simplifying x = 8.227620379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1725.772379621, 8.227620379}

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