-4.9x^2+32x+0.2=0

Solution for -4.9x^2+32x+0.2=0 equation:

Simplifying
-4.9x2 + 32x + 0.2 = 0

Reorder the terms:
0.2 + 32x + -4.9x2 = 0

Solving
0.2 + 32x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-0.04081632653 + -6.530612245x + x2 = 0

Move the constant term to the right:

Add '0.04081632653' to each side of the equation.
-0.04081632653 + -6.530612245x + 0.04081632653 + x2 = 0 + 0.04081632653

Reorder the terms:
-0.04081632653 + 0.04081632653 + -6.530612245x + x2 = 0 + 0.04081632653

Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000
0.00000000000 + -6.530612245x + x2 = 0 + 0.04081632653
-6.530612245x + x2 = 0 + 0.04081632653

Combine like terms: 0 + 0.04081632653 = 0.04081632653
-6.530612245x + x2 = 0.04081632653

The x term is -6.530612245x.  Take half its coefficient (-3.265306123).
Square it (10.66222408) and add it to both sides.

Add '10.66222408' to each side of the equation.
-6.530612245x + 10.66222408 + x2 = 0.04081632653 + 10.66222408

Reorder the terms:
10.66222408 + -6.530612245x + x2 = 0.04081632653 + 10.66222408

Combine like terms: 0.04081632653 + 10.66222408 = 10.70304040653
10.66222408 + -6.530612245x + x2 = 10.70304040653

Factor a perfect square on the left side:
(x + -3.265306123)(x + -3.265306123) = 10.70304040653

Calculate the square root of the right side: 3.271550153

Break this problem into two subproblems by setting 
(x + -3.265306123) equal to 3.271550153 and -3.271550153.

Subproblem 1
x + -3.265306123 = 3.271550153

Simplifying
x + -3.265306123 = 3.271550153

Reorder the terms:
-3.265306123 + x = 3.271550153

Solving
-3.265306123 + x = 3.271550153

Solving for variable 'x'.

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

Add '3.265306123' to each side of the equation.
-3.265306123 + 3.265306123 + x = 3.271550153 + 3.265306123

Combine like terms: -3.265306123 + 3.265306123 = 0.000000000
0.000000000 + x = 3.271550153 + 3.265306123
x = 3.271550153 + 3.265306123

Combine like terms: 3.271550153 + 3.265306123 = 6.536856276
x = 6.536856276

Simplifying
x = 6.536856276

Subproblem 2
x + -3.265306123 = -3.271550153

Simplifying
x + -3.265306123 = -3.271550153

Reorder the terms:
-3.265306123 + x = -3.271550153

Solving
-3.265306123 + x = -3.271550153

Solving for variable 'x'.

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

Add '3.265306123' to each side of the equation.
-3.265306123 + 3.265306123 + x = -3.271550153 + 3.265306123

Combine like terms: -3.265306123 + 3.265306123 = 0.000000000
0.000000000 + x = -3.271550153 + 3.265306123
x = -3.271550153 + 3.265306123

Combine like terms: -3.271550153 + 3.265306123 = -0.00624403
x = -0.00624403

Simplifying
x = -0.00624403

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.536856276, -0.00624403}