x^2-13x-42=0

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

Simplifying
x2 + -13x + -42 = 0

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

Solving
-42 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

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 = 15.678779875
x = 15.678779875

Simplifying
x = 15.678779875

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 = -2.678779875
x = -2.678779875

Simplifying
x = -2.678779875

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