x^2+1.6x-0.5=0

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Solution for x^2+1.6x-0.5=0 equation: 


Simplifying
x2 + 1.6x + -0.5 = 0

Reorder the terms:
-0.5 + 1.6x + x2 = 0

Solving
-0.5 + 1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.6x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.6x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.6x + x2 = 0 + 0.5
1.6x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.6x + x2 = 0.5

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.5 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.5 + 0.64

Combine like terms: 0.5 + 0.64 = 1.14
0.64 + 1.6x + x2 = 1.14

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 1.14

Calculate the square root of the right side: 1.067707825

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.067707825 and -1.067707825.


Subproblem 1
x + 0.8 = 1.067707825

Simplifying
x + 0.8 = 1.067707825

Reorder the terms:
0.8 + x = 1.067707825

Solving
0.8 + x = 1.067707825

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 1.067707825 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 1.067707825 + -0.8
x = 1.067707825 + -0.8

Combine like terms: 1.067707825 + -0.8 = 0.267707825
x = 0.267707825

Simplifying
x = 0.267707825


Subproblem 2
x + 0.8 = -1.067707825

Simplifying
x + 0.8 = -1.067707825

Reorder the terms:
0.8 + x = -1.067707825

Solving
0.8 + x = -1.067707825

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -1.067707825 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -1.067707825 + -0.8
x = -1.067707825 + -0.8

Combine like terms: -1.067707825 + -0.8 = -1.867707825
x = -1.867707825

Simplifying
x = -1.867707825


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.267707825, -1.867707825}

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