x^2+13x-39=0

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Solution for x^2+13x-39=0 equation:


Simplifying
x2 + 13x + -39 = 0

Reorder the terms:
-39 + 13x + x2 = 0

Solving
-39 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 13x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + 13x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 13x + x2 = 0 + 39
13x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
13x + x2 = 39

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 = 39 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 39 + 42.25

Combine like terms: 39 + 42.25 = 81.25
42.25 + 13x + x2 = 81.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + 6.5) equal to 9.013878189 and -9.013878189.

Subproblem 1

x + 6.5 = 9.013878189 Simplifying x + 6.5 = 9.013878189 Reorder the terms: 6.5 + x = 9.013878189 Solving 6.5 + x = 9.013878189 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 = 9.013878189 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.013878189 + -6.5 x = 9.013878189 + -6.5 Combine like terms: 9.013878189 + -6.5 = 2.513878189 x = 2.513878189 Simplifying x = 2.513878189

Subproblem 2

x + 6.5 = -9.013878189 Simplifying x + 6.5 = -9.013878189 Reorder the terms: 6.5 + x = -9.013878189 Solving 6.5 + x = -9.013878189 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 = -9.013878189 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.013878189 + -6.5 x = -9.013878189 + -6.5 Combine like terms: -9.013878189 + -6.5 = -15.513878189 x = -15.513878189 Simplifying x = -15.513878189

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.513878189, -15.513878189}

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