x^2+13x-2=0

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


Simplifying
x2 + 13x + -2 = 0

Reorder the terms:
-2 + 13x + x2 = 0

Solving
-2 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 13x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 13x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 13x + x2 = 0 + 2
13x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
13x + x2 = 2

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 = 2 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 2 + 42.25

Combine like terms: 2 + 42.25 = 44.25
42.25 + 13x + x2 = 44.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.652067348 and -6.652067348.


Subproblem 1
x + 6.5 = 6.652067348

Simplifying
x + 6.5 = 6.652067348

Reorder the terms:
6.5 + x = 6.652067348

Solving
6.5 + x = 6.652067348

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 = 6.652067348 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.652067348 + -6.5
x = 6.652067348 + -6.5

Combine like terms: 6.652067348 + -6.5 = 0.152067348
x = 0.152067348

Simplifying
x = 0.152067348


Subproblem 2
x + 6.5 = -6.652067348

Simplifying
x + 6.5 = -6.652067348

Reorder the terms:
6.5 + x = -6.652067348

Solving
6.5 + x = -6.652067348

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 = -6.652067348 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.652067348 + -6.5
x = -6.652067348 + -6.5

Combine like terms: -6.652067348 + -6.5 = -13.152067348
x = -13.152067348

Simplifying
x = -13.152067348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.152067348, -13.152067348}

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