2.8x^2+32x-5=0

Solution for 2.8x^2+32x-5=0 equation:

Simplifying
2.8x2 + 32x + -5 = 0

Reorder the terms:
-5 + 32x + 2.8x2 = 0

Solving
-5 + 32x + 2.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2.8 the coefficient of the squared term: 

Divide each side by '2.8'.
-1.785714286 + 11.42857143x + x2 = 0

Move the constant term to the right:

Add '1.785714286' to each side of the equation.
-1.785714286 + 11.42857143x + 1.785714286 + x2 = 0 + 1.785714286

Reorder the terms:
-1.785714286 + 1.785714286 + 11.42857143x + x2 = 0 + 1.785714286

Combine like terms: -1.785714286 + 1.785714286 = 0.000000000
0.000000000 + 11.42857143x + x2 = 0 + 1.785714286
11.42857143x + x2 = 0 + 1.785714286

Combine like terms: 0 + 1.785714286 = 1.785714286
11.42857143x + x2 = 1.785714286

The x term is 11.42857143x.  Take half its coefficient (5.714285715).
Square it (32.65306123) and add it to both sides.

Add '32.65306123' to each side of the equation.
11.42857143x + 32.65306123 + x2 = 1.785714286 + 32.65306123

Reorder the terms:
32.65306123 + 11.42857143x + x2 = 1.785714286 + 32.65306123

Combine like terms: 1.785714286 + 32.65306123 = 34.438775516
32.65306123 + 11.42857143x + x2 = 34.438775516

Factor a perfect square on the left side:
(x + 5.714285715)(x + 5.714285715) = 34.438775516

Calculate the square root of the right side: 5.868455974

Break this problem into two subproblems by setting 
(x + 5.714285715) equal to 5.868455974 and -5.868455974.

Subproblem 1
x + 5.714285715 = 5.868455974

Simplifying
x + 5.714285715 = 5.868455974

Reorder the terms:
5.714285715 + x = 5.868455974

Solving
5.714285715 + x = 5.868455974

Solving for variable 'x'.

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

Add '-5.714285715' to each side of the equation.
5.714285715 + -5.714285715 + x = 5.868455974 + -5.714285715

Combine like terms: 5.714285715 + -5.714285715 = 0.000000000
0.000000000 + x = 5.868455974 + -5.714285715
x = 5.868455974 + -5.714285715

Combine like terms: 5.868455974 + -5.714285715 = 0.154170259
x = 0.154170259

Simplifying
x = 0.154170259

Subproblem 2
x + 5.714285715 = -5.868455974

Simplifying
x + 5.714285715 = -5.868455974

Reorder the terms:
5.714285715 + x = -5.868455974

Solving
5.714285715 + x = -5.868455974

Solving for variable 'x'.

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

Add '-5.714285715' to each side of the equation.
5.714285715 + -5.714285715 + x = -5.868455974 + -5.714285715

Combine like terms: 5.714285715 + -5.714285715 = 0.000000000
0.000000000 + x = -5.868455974 + -5.714285715
x = -5.868455974 + -5.714285715

Combine like terms: -5.868455974 + -5.714285715 = -11.582741689
x = -11.582741689

Simplifying
x = -11.582741689

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.154170259, -11.582741689}