x^2+0.8x+0.1=0

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Solution for x^2+0.8x+0.1=0 equation: 


Simplifying
x2 + 0.8x + 0.1 = 0

Reorder the terms:
0.1 + 0.8x + x2 = 0

Solving
0.1 + 0.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 0.8x + -0.1 + x2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + 0.8x + x2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 0.8x + x2 = 0 + -0.1
0.8x + x2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
0.8x + x2 = -0.1

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = -0.1 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = -0.1 + 0.16

Combine like terms: -0.1 + 0.16 = 0.06
0.16 + 0.8x + x2 = 0.06

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.06

Calculate the square root of the right side: 0.244948974

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.244948974 and -0.244948974.


Subproblem 1
x + 0.4 = 0.244948974

Simplifying
x + 0.4 = 0.244948974

Reorder the terms:
0.4 + x = 0.244948974

Solving
0.4 + x = 0.244948974

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 0.244948974 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.244948974 + -0.4
x = 0.244948974 + -0.4

Combine like terms: 0.244948974 + -0.4 = -0.155051026
x = -0.155051026

Simplifying
x = -0.155051026


Subproblem 2
x + 0.4 = -0.244948974

Simplifying
x + 0.4 = -0.244948974

Reorder the terms:
0.4 + x = -0.244948974

Solving
0.4 + x = -0.244948974

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -0.244948974 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -0.244948974 + -0.4
x = -0.244948974 + -0.4

Combine like terms: -0.244948974 + -0.4 = -0.644948974
x = -0.644948974

Simplifying
x = -0.644948974


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.155051026, -0.644948974}

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