0=x^2+13x-42

Solution for 0=x^2+13x-42 equation:

Simplifying
0 = x2 + 13x + -42

Reorder the terms:
0 = -42 + 13x + x2

Solving
0 = -42 + 13x + x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + -13x + -1x2 = -42 + 13x + x2 + 42 + -13x + -1x2

Reorder the terms:
42 + -13x + -1x2 = -42 + 42 + 13x + -13x + x2 + -1x2

Combine like terms: -42 + 42 = 0
42 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
42 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
42 + -13x + -1x2 = 0 + x2 + -1x2
42 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + -13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-42 + 13x + x2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 13x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 13x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 13x + x2 = 0 + 42
13x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
13x + x2 = 42

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 = 42 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 42 + 42.25

Combine like terms: 42 + 42.25 = 84.25
42.25 + 13x + x2 = 84.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + 6.5) equal to 9.178779875 and -9.178779875.

Subproblem 1
x + 6.5 = 9.178779875

Simplifying
x + 6.5 = 9.178779875

Reorder the terms:
6.5 + x = 9.178779875

Solving
6.5 + x = 9.178779875

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 = 9.178779875 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 9.178779875 + -6.5
x = 9.178779875 + -6.5

Combine like terms: 9.178779875 + -6.5 = 2.678779875
x = 2.678779875

Simplifying
x = 2.678779875

Subproblem 2
x + 6.5 = -9.178779875

Simplifying
x + 6.5 = -9.178779875

Reorder the terms:
6.5 + x = -9.178779875

Solving
6.5 + x = -9.178779875

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 = -9.178779875 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -9.178779875 + -6.5
x = -9.178779875 + -6.5

Combine like terms: -9.178779875 + -6.5 = -15.678779875
x = -15.678779875

Simplifying
x = -15.678779875

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.678779875, -15.678779875}