4.9x^2-32x-0.5=0

Solution for 4.9x^2-32x-0.5=0 equation:

Simplifying
4.9x2 + -32x + -0.5 = 0

Reorder the terms:
-0.5 + -32x + 4.9x2 = 0

Solving
-0.5 + -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'.
-0.1020408163 + -6.530612245x + x2 = 0

Move the constant term to the right:

Add '0.1020408163' to each side of the equation.
-0.1020408163 + -6.530612245x + 0.1020408163 + x2 = 0 + 0.1020408163

Reorder the terms:
-0.1020408163 + 0.1020408163 + -6.530612245x + x2 = 0 + 0.1020408163

Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000
0.0000000000 + -6.530612245x + x2 = 0 + 0.1020408163
-6.530612245x + x2 = 0 + 0.1020408163

Combine like terms: 0 + 0.1020408163 = 0.1020408163
-6.530612245x + x2 = 0.1020408163

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 = 0.1020408163 + 10.66222408

Reorder the terms:
10.66222408 + -6.530612245x + x2 = 0.1020408163 + 10.66222408

Combine like terms: 0.1020408163 + 10.66222408 = 10.7642648963
10.66222408 + -6.530612245x + x2 = 10.7642648963

Factor a perfect square on the left side:
(x + -3.265306123)(x + -3.265306123) = 10.7642648963

Calculate the square root of the right side: 3.280893917

Break this problem into two subproblems by setting 
(x + -3.265306123) equal to 3.280893917 and -3.280893917.

Subproblem 1
x + -3.265306123 = 3.280893917

Simplifying
x + -3.265306123 = 3.280893917

Reorder the terms:
-3.265306123 + x = 3.280893917

Solving
-3.265306123 + x = 3.280893917

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 = 3.280893917 + 3.265306123

Combine like terms: -3.265306123 + 3.265306123 = 0.000000000
0.000000000 + x = 3.280893917 + 3.265306123
x = 3.280893917 + 3.265306123

Combine like terms: 3.280893917 + 3.265306123 = 6.54620004
x = 6.54620004

Simplifying
x = 6.54620004

Subproblem 2
x + -3.265306123 = -3.280893917

Simplifying
x + -3.265306123 = -3.280893917

Reorder the terms:
-3.265306123 + x = -3.280893917

Solving
-3.265306123 + x = -3.280893917

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 = -3.280893917 + 3.265306123

Combine like terms: -3.265306123 + 3.265306123 = 0.000000000
0.000000000 + x = -3.280893917 + 3.265306123
x = -3.280893917 + 3.265306123

Combine like terms: -3.280893917 + 3.265306123 = -0.015587794
x = -0.015587794

Simplifying
x = -0.015587794

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.54620004, -0.015587794}