x^2-3x-20=0.2

Solution for x^2-3x-20=0.2 equation:

Simplifying
x2 + -3x + -20 = 0.2

Reorder the terms:
-20 + -3x + x2 = 0.2

Solving
-20 + -3x + x2 = 0.2

Solving for variable 'x'.

Reorder the terms:
-20 + -0.2 + -3x + x2 = 0.2 + -0.2

Combine like terms: -20 + -0.2 = -20.2
-20.2 + -3x + x2 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
-20.2 + -3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '20.2' to each side of the equation.
-20.2 + -3x + 20.2 + x2 = 0.0 + 20.2

Reorder the terms:
-20.2 + 20.2 + -3x + x2 = 0.0 + 20.2

Combine like terms: -20.2 + 20.2 = 0.0
0.0 + -3x + x2 = 0.0 + 20.2
-3x + x2 = 0.0 + 20.2

Combine like terms: 0.0 + 20.2 = 20.2
-3x + x2 = 20.2

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 20.2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 20.2 + 2.25

Combine like terms: 20.2 + 2.25 = 22.45
2.25 + -3x + x2 = 22.45

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 22.45

Calculate the square root of the right side: 4.738143096

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.738143096 and -4.738143096.

Subproblem 1
x + -1.5 = 4.738143096

Simplifying
x + -1.5 = 4.738143096

Reorder the terms:
-1.5 + x = 4.738143096

Solving
-1.5 + x = 4.738143096

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.738143096 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.738143096 + 1.5
x = 4.738143096 + 1.5

Combine like terms: 4.738143096 + 1.5 = 6.238143096
x = 6.238143096

Simplifying
x = 6.238143096

Subproblem 2
x + -1.5 = -4.738143096

Simplifying
x + -1.5 = -4.738143096

Reorder the terms:
-1.5 + x = -4.738143096

Solving
-1.5 + x = -4.738143096

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.738143096 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.738143096 + 1.5
x = -4.738143096 + 1.5

Combine like terms: -4.738143096 + 1.5 = -3.238143096
x = -3.238143096

Simplifying
x = -3.238143096

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.238143096, -3.238143096}