x^2-.2x-8.4=0

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Solution for x^2-.2x-8.4=0 equation: 


Simplifying
x2 + -0.2x + -8.4 = 0

Reorder the terms:
-8.4 + -0.2x + x2 = 0

Solving
-8.4 + -0.2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8.4' to each side of the equation.
-8.4 + -0.2x + 8.4 + x2 = 0 + 8.4

Reorder the terms:
-8.4 + 8.4 + -0.2x + x2 = 0 + 8.4

Combine like terms: -8.4 + 8.4 = 0.0
0.0 + -0.2x + x2 = 0 + 8.4
-0.2x + x2 = 0 + 8.4

Combine like terms: 0 + 8.4 = 8.4
-0.2x + x2 = 8.4

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = 8.4 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = 8.4 + 0.01

Combine like terms: 8.4 + 0.01 = 8.41
0.01 + -0.2x + x2 = 8.41

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = 8.41

Calculate the square root of the right side: 2.9

Break this problem into two subproblems by setting 
(x + -0.1) equal to 2.9 and -2.9.


Subproblem 1
x + -0.1 = 2.9

Simplifying
x + -0.1 = 2.9

Reorder the terms:
-0.1 + x = 2.9

Solving
-0.1 + x = 2.9

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = 2.9 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = 2.9 + 0.1
x = 2.9 + 0.1

Combine like terms: 2.9 + 0.1 = 3
x = 3

Simplifying
x = 3


Subproblem 2
x + -0.1 = -2.9

Simplifying
x + -0.1 = -2.9

Reorder the terms:
-0.1 + x = -2.9

Solving
-0.1 + x = -2.9

Solving for variable 'x'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + x = -2.9 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + x = -2.9 + 0.1
x = -2.9 + 0.1

Combine like terms: -2.9 + 0.1 = -2.8
x = -2.8

Simplifying
x = -2.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -2.8}

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