x^2-27x-42=0

Solution for x^2-27x-42=0 equation:

Simplifying
x2 + -27x + -42 = 0

Reorder the terms:
-42 + -27x + x2 = 0

Solving
-42 + -27x + 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 + -27x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -27x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -27x + x2 = 0 + 42
-27x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-27x + x2 = 42

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = 42 + 182.25

Reorder the terms:
182.25 + -27x + x2 = 42 + 182.25

Combine like terms: 42 + 182.25 = 224.25
182.25 + -27x + x2 = 224.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 224.25

Calculate the square root of the right side: 14.974979132

Break this problem into two subproblems by setting 
(x + -13.5) equal to 14.974979132 and -14.974979132.

Subproblem 1
x + -13.5 = 14.974979132

Simplifying
x + -13.5 = 14.974979132

Reorder the terms:
-13.5 + x = 14.974979132

Solving
-13.5 + x = 14.974979132

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 14.974979132 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 14.974979132 + 13.5
x = 14.974979132 + 13.5

Combine like terms: 14.974979132 + 13.5 = 28.474979132
x = 28.474979132

Simplifying
x = 28.474979132

Subproblem 2
x + -13.5 = -14.974979132

Simplifying
x + -13.5 = -14.974979132

Reorder the terms:
-13.5 + x = -14.974979132

Solving
-13.5 + x = -14.974979132

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -14.974979132 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -14.974979132 + 13.5
x = -14.974979132 + 13.5

Combine like terms: -14.974979132 + 13.5 = -1.474979132
x = -1.474979132

Simplifying
x = -1.474979132

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.474979132, -1.474979132}