x^2-.4x-27=0

Solution for x^2-.4x-27=0 equation:

Simplifying
x2 + -0.4x + -27 = 0

Reorder the terms:
-27 + -0.4x + x2 = 0

Solving
-27 + -0.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -0.4x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -0.4x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -0.4x + x2 = 0 + 27
-0.4x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-0.4x + x2 = 27

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 27 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 27 + 0.04

Combine like terms: 27 + 0.04 = 27.04
0.04 + -0.4x + x2 = 27.04

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 27.04

Calculate the square root of the right side: 5.2

Break this problem into two subproblems by setting 
(x + -0.2) equal to 5.2 and -5.2.

Subproblem 1
x + -0.2 = 5.2

Simplifying
x + -0.2 = 5.2

Reorder the terms:
-0.2 + x = 5.2

Solving
-0.2 + x = 5.2

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 5.2 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 5.2 + 0.2
x = 5.2 + 0.2

Combine like terms: 5.2 + 0.2 = 5.4
x = 5.4

Simplifying
x = 5.4

Subproblem 2
x + -0.2 = -5.2

Simplifying
x + -0.2 = -5.2

Reorder the terms:
-0.2 + x = -5.2

Solving
-0.2 + x = -5.2

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -5.2 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -5.2 + 0.2
x = -5.2 + 0.2

Combine like terms: -5.2 + 0.2 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.4, -5}