.8-34x-1.25x^2=0

Solution for .8-34x-1.25x^2=0 equation:

Simplifying
0.8 + -34x + -1.25x2 = 0

Solving
0.8 + -34x + -1.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.25 the coefficient of the squared term: 

Divide each side by '-1.25'.
-0.64 + 27.2x + x2 = 0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + 27.2x + 0.64 + x2 = 0 + 0.64

Reorder the terms:
-0.64 + 0.64 + 27.2x + x2 = 0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + 27.2x + x2 = 0 + 0.64
27.2x + x2 = 0 + 0.64

Combine like terms: 0 + 0.64 = 0.64
27.2x + x2 = 0.64

The x term is 27.2x.  Take half its coefficient (13.6).
Square it (184.96) and add it to both sides.

Add '184.96' to each side of the equation.
27.2x + 184.96 + x2 = 0.64 + 184.96

Reorder the terms:
184.96 + 27.2x + x2 = 0.64 + 184.96

Combine like terms: 0.64 + 184.96 = 185.6
184.96 + 27.2x + x2 = 185.6

Factor a perfect square on the left side:
(x + 13.6)(x + 13.6) = 185.6

Calculate the square root of the right side: 13.623509093

Break this problem into two subproblems by setting 
(x + 13.6) equal to 13.623509093 and -13.623509093.

Subproblem 1
x + 13.6 = 13.623509093

Simplifying
x + 13.6 = 13.623509093

Reorder the terms:
13.6 + x = 13.623509093

Solving
13.6 + x = 13.623509093

Solving for variable 'x'.

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

Add '-13.6' to each side of the equation.
13.6 + -13.6 + x = 13.623509093 + -13.6

Combine like terms: 13.6 + -13.6 = 0.0
0.0 + x = 13.623509093 + -13.6
x = 13.623509093 + -13.6

Combine like terms: 13.623509093 + -13.6 = 0.023509093
x = 0.023509093

Simplifying
x = 0.023509093

Subproblem 2
x + 13.6 = -13.623509093

Simplifying
x + 13.6 = -13.623509093

Reorder the terms:
13.6 + x = -13.623509093

Solving
13.6 + x = -13.623509093

Solving for variable 'x'.

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

Add '-13.6' to each side of the equation.
13.6 + -13.6 + x = -13.623509093 + -13.6

Combine like terms: 13.6 + -13.6 = 0.0
0.0 + x = -13.623509093 + -13.6
x = -13.623509093 + -13.6

Combine like terms: -13.623509093 + -13.6 = -27.223509093
x = -27.223509093

Simplifying
x = -27.223509093

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.023509093, -27.223509093}