x^2-169x-849=0

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Solution for x^2-169x-849=0 equation:


Simplifying
x2 + -169x + -849 = 0

Reorder the terms:
-849 + -169x + x2 = 0

Solving
-849 + -169x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '849' to each side of the equation.
-849 + -169x + 849 + x2 = 0 + 849

Reorder the terms:
-849 + 849 + -169x + x2 = 0 + 849

Combine like terms: -849 + 849 = 0
0 + -169x + x2 = 0 + 849
-169x + x2 = 0 + 849

Combine like terms: 0 + 849 = 849
-169x + x2 = 849

The x term is -169x.  Take half its coefficient (-84.5).
Square it (7140.25) and add it to both sides.

Add '7140.25' to each side of the equation.
-169x + 7140.25 + x2 = 849 + 7140.25

Reorder the terms:
7140.25 + -169x + x2 = 849 + 7140.25

Combine like terms: 849 + 7140.25 = 7989.25
7140.25 + -169x + x2 = 7989.25

Factor a perfect square on the left side:
(x + -84.5)(x + -84.5) = 7989.25

Calculate the square root of the right side: 89.382604572

Break this problem into two subproblems by setting 
(x + -84.5) equal to 89.382604572 and -89.382604572.

Subproblem 1

x + -84.5 = 89.382604572 Simplifying x + -84.5 = 89.382604572 Reorder the terms: -84.5 + x = 89.382604572 Solving -84.5 + x = 89.382604572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + x = 89.382604572 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + x = 89.382604572 + 84.5 x = 89.382604572 + 84.5 Combine like terms: 89.382604572 + 84.5 = 173.882604572 x = 173.882604572 Simplifying x = 173.882604572

Subproblem 2

x + -84.5 = -89.382604572 Simplifying x + -84.5 = -89.382604572 Reorder the terms: -84.5 + x = -89.382604572 Solving -84.5 + x = -89.382604572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + x = -89.382604572 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + x = -89.382604572 + 84.5 x = -89.382604572 + 84.5 Combine like terms: -89.382604572 + 84.5 = -4.882604572 x = -4.882604572 Simplifying x = -4.882604572

Solution

The solution to the problem is based on the solutions from the subproblems. x = {173.882604572, -4.882604572}

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