x^2+1.6x-2.8=0

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Solution for x^2+1.6x-2.8=0 equation: 


Simplifying
x2 + 1.6x + -2.8 = 0

Reorder the terms:
-2.8 + 1.6x + x2 = 0

Solving
-2.8 + 1.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + 1.6x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + 1.6x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + 1.6x + x2 = 0 + 2.8
1.6x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
1.6x + x2 = 2.8

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 = 2.8 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 2.8 + 0.64

Combine like terms: 2.8 + 0.64 = 3.44
0.64 + 1.6x + x2 = 3.44

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 3.44

Calculate the square root of the right side: 1.854723699

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.854723699 and -1.854723699.


Subproblem 1
x + 0.8 = 1.854723699

Simplifying
x + 0.8 = 1.854723699

Reorder the terms:
0.8 + x = 1.854723699

Solving
0.8 + x = 1.854723699

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 = 1.854723699 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 1.854723699 + -0.8
x = 1.854723699 + -0.8

Combine like terms: 1.854723699 + -0.8 = 1.054723699
x = 1.054723699

Simplifying
x = 1.054723699


Subproblem 2
x + 0.8 = -1.854723699

Simplifying
x + 0.8 = -1.854723699

Reorder the terms:
0.8 + x = -1.854723699

Solving
0.8 + x = -1.854723699

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 = -1.854723699 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -1.854723699 + -0.8
x = -1.854723699 + -0.8

Combine like terms: -1.854723699 + -0.8 = -2.654723699
x = -2.654723699

Simplifying
x = -2.654723699


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.054723699, -2.654723699}

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