4.9x^2-60x+56.25=0

Solution for 4.9x^2-60x+56.25=0 equation:

Simplifying
4.9x2 + -60x + 56.25 = 0

Reorder the terms:
56.25 + -60x + 4.9x2 = 0

Solving
56.25 + -60x + 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'.
11.47959184 + -12.24489796x + x2 = 0

Move the constant term to the right:

Add '-11.47959184' to each side of the equation.
11.47959184 + -12.24489796x + -11.47959184 + x2 = 0 + -11.47959184

Reorder the terms:
11.47959184 + -11.47959184 + -12.24489796x + x2 = 0 + -11.47959184

Combine like terms: 11.47959184 + -11.47959184 = 0.00000000
0.00000000 + -12.24489796x + x2 = 0 + -11.47959184
-12.24489796x + x2 = 0 + -11.47959184

Combine like terms: 0 + -11.47959184 = -11.47959184
-12.24489796x + x2 = -11.47959184

The x term is -12.24489796x.  Take half its coefficient (-6.12244898).
Square it (37.48438151) and add it to both sides.

Add '37.48438151' to each side of the equation.
-12.24489796x + 37.48438151 + x2 = -11.47959184 + 37.48438151

Reorder the terms:
37.48438151 + -12.24489796x + x2 = -11.47959184 + 37.48438151

Combine like terms: -11.47959184 + 37.48438151 = 26.00478967
37.48438151 + -12.24489796x + x2 = 26.00478967

Factor a perfect square on the left side:
(x + -6.12244898)(x + -6.12244898) = 26.00478967

Calculate the square root of the right side: 5.099489158

Break this problem into two subproblems by setting 
(x + -6.12244898) equal to 5.099489158 and -5.099489158.

Subproblem 1
x + -6.12244898 = 5.099489158

Simplifying
x + -6.12244898 = 5.099489158

Reorder the terms:
-6.12244898 + x = 5.099489158

Solving
-6.12244898 + x = 5.099489158

Solving for variable 'x'.

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

Add '6.12244898' to each side of the equation.
-6.12244898 + 6.12244898 + x = 5.099489158 + 6.12244898

Combine like terms: -6.12244898 + 6.12244898 = 0.00000000
0.00000000 + x = 5.099489158 + 6.12244898
x = 5.099489158 + 6.12244898

Combine like terms: 5.099489158 + 6.12244898 = 11.221938138
x = 11.221938138

Simplifying
x = 11.221938138

Subproblem 2
x + -6.12244898 = -5.099489158

Simplifying
x + -6.12244898 = -5.099489158

Reorder the terms:
-6.12244898 + x = -5.099489158

Solving
-6.12244898 + x = -5.099489158

Solving for variable 'x'.

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

Add '6.12244898' to each side of the equation.
-6.12244898 + 6.12244898 + x = -5.099489158 + 6.12244898

Combine like terms: -6.12244898 + 6.12244898 = 0.00000000
0.00000000 + x = -5.099489158 + 6.12244898
x = -5.099489158 + 6.12244898

Combine like terms: -5.099489158 + 6.12244898 = 1.022959822
x = 1.022959822

Simplifying
x = 1.022959822

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.221938138, 1.022959822}