x^2+13x+13=0

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


Simplifying
x2 + 13x + 13 = 0

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

Solving
13 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -13 + 42.25

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

Combine like terms: -13 + 42.25 = 29.25
42.25 + 13x + x2 = 29.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + 6.5) equal to 5.408326913 and -5.408326913.

Subproblem 1

x + 6.5 = 5.408326913 Simplifying x + 6.5 = 5.408326913 Reorder the terms: 6.5 + x = 5.408326913 Solving 6.5 + x = 5.408326913 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 = 5.408326913 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 5.408326913 + -6.5 x = 5.408326913 + -6.5 Combine like terms: 5.408326913 + -6.5 = -1.091673087 x = -1.091673087 Simplifying x = -1.091673087

Subproblem 2

x + 6.5 = -5.408326913 Simplifying x + 6.5 = -5.408326913 Reorder the terms: 6.5 + x = -5.408326913 Solving 6.5 + x = -5.408326913 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 = -5.408326913 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -5.408326913 + -6.5 x = -5.408326913 + -6.5 Combine like terms: -5.408326913 + -6.5 = -11.908326913 x = -11.908326913 Simplifying x = -11.908326913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.091673087, -11.908326913}

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