0.16+0.8x+x^2=0

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Solution for 0.16+0.8x+x^2=0 equation: 


Simplifying
0.16 + 0.8x + x2 = 0

Solving
0.16 + 0.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + 0.8x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + 0.8x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + 0.8x + x2 = 0 + -0.16
0.8x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
0.8x + x2 = -0.16

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 = -0.16 + 0.16

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

Combine like terms: -0.16 + 0.16 = 0.00
0.16 + 0.8x + x2 = 0.00

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 0.4) equal to 0.00 and 0.00.


Subproblem 1
x + 0.4 = 0.00

Simplifying
x + 0.4 = 0.00

Reorder the terms:
0.4 + x = 0.00

Solving
0.4 + x = 0.00

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 = 0.00 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.00 + -0.4
x = 0.00 + -0.4

Combine like terms: 0.00 + -0.4 = -0.4
x = -0.4

Simplifying
x = -0.4


Subproblem 2
x + 0.4 = 0.00

Simplifying
x + 0.4 = 0.00

Reorder the terms:
0.4 + x = 0.00

Solving
0.4 + x = 0.00

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 = 0.00 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 0.00 + -0.4
x = 0.00 + -0.4

Combine like terms: 0.00 + -0.4 = -0.4
x = -0.4

Simplifying
x = -0.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.4, -0.4}

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