4.9x^2+30x-500=0

Solution for 4.9x^2+30x-500=0 equation:

Simplifying
4.9x2 + 30x + -500 = 0

Reorder the terms:
-500 + 30x + 4.9x2 = 0

Solving
-500 + 30x + 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'.
-102.0408163 + 6.12244898x + x2 = 0

Move the constant term to the right:

Add '102.0408163' to each side of the equation.
-102.0408163 + 6.12244898x + 102.0408163 + x2 = 0 + 102.0408163

Reorder the terms:
-102.0408163 + 102.0408163 + 6.12244898x + x2 = 0 + 102.0408163

Combine like terms: -102.0408163 + 102.0408163 = 0.0000000
0.0000000 + 6.12244898x + x2 = 0 + 102.0408163
6.12244898x + x2 = 0 + 102.0408163

Combine like terms: 0 + 102.0408163 = 102.0408163
6.12244898x + x2 = 102.0408163

The x term is 6.12244898x.  Take half its coefficient (3.06122449).
Square it (9.371095378) and add it to both sides.

Add '9.371095378' to each side of the equation.
6.12244898x + 9.371095378 + x2 = 102.0408163 + 9.371095378

Reorder the terms:
9.371095378 + 6.12244898x + x2 = 102.0408163 + 9.371095378

Combine like terms: 102.0408163 + 9.371095378 = 111.411911678
9.371095378 + 6.12244898x + x2 = 111.411911678

Factor a perfect square on the left side:
(x + 3.06122449)(x + 3.06122449) = 111.411911678

Calculate the square root of the right side: 10.555184114

Break this problem into two subproblems by setting 
(x + 3.06122449) equal to 10.555184114 and -10.555184114.

Subproblem 1
x + 3.06122449 = 10.555184114

Simplifying
x + 3.06122449 = 10.555184114

Reorder the terms:
3.06122449 + x = 10.555184114

Solving
3.06122449 + x = 10.555184114

Solving for variable 'x'.

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

Add '-3.06122449' to each side of the equation.
3.06122449 + -3.06122449 + x = 10.555184114 + -3.06122449

Combine like terms: 3.06122449 + -3.06122449 = 0.00000000
0.00000000 + x = 10.555184114 + -3.06122449
x = 10.555184114 + -3.06122449

Combine like terms: 10.555184114 + -3.06122449 = 7.493959624
x = 7.493959624

Simplifying
x = 7.493959624

Subproblem 2
x + 3.06122449 = -10.555184114

Simplifying
x + 3.06122449 = -10.555184114

Reorder the terms:
3.06122449 + x = -10.555184114

Solving
3.06122449 + x = -10.555184114

Solving for variable 'x'.

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

Add '-3.06122449' to each side of the equation.
3.06122449 + -3.06122449 + x = -10.555184114 + -3.06122449

Combine like terms: 3.06122449 + -3.06122449 = 0.00000000
0.00000000 + x = -10.555184114 + -3.06122449
x = -10.555184114 + -3.06122449

Combine like terms: -10.555184114 + -3.06122449 = -13.616408604
x = -13.616408604

Simplifying
x = -13.616408604

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.493959624, -13.616408604}