x^2-13x-102=0

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Solution for x^2-13x-102=0 equation:


Simplifying
x2 + -13x + -102 = 0

Reorder the terms:
-102 + -13x + x2 = 0

Solving
-102 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + -13x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + -13x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -13x + x2 = 0 + 102
-13x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
-13x + x2 = 102

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 102 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 102 + 42.25

Combine like terms: 102 + 42.25 = 144.25
42.25 + -13x + x2 = 144.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(x + -6.5) equal to 12.010412149 and -12.010412149.

Subproblem 1

x + -6.5 = 12.010412149 Simplifying x + -6.5 = 12.010412149 Reorder the terms: -6.5 + x = 12.010412149 Solving -6.5 + x = 12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 12.010412149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 12.010412149 + 6.5 x = 12.010412149 + 6.5 Combine like terms: 12.010412149 + 6.5 = 18.510412149 x = 18.510412149 Simplifying x = 18.510412149

Subproblem 2

x + -6.5 = -12.010412149 Simplifying x + -6.5 = -12.010412149 Reorder the terms: -6.5 + x = -12.010412149 Solving -6.5 + x = -12.010412149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -12.010412149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -12.010412149 + 6.5 x = -12.010412149 + 6.5 Combine like terms: -12.010412149 + 6.5 = -5.510412149 x = -5.510412149 Simplifying x = -5.510412149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.510412149, -5.510412149}

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