-4.905x^2+11x-1.4=0

Solution for -4.905x^2+11x-1.4=0 equation:

Simplifying
-4.905x2 + 11x + -1.4 = 0

Reorder the terms:
-1.4 + 11x + -4.905x2 = 0

Solving
-1.4 + 11x + -4.905x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.905 the coefficient of the squared term: 

Divide each side by '-4.905'.
0.2854230377 + -2.242609582x + x2 = 0

Move the constant term to the right:

Add '-0.2854230377' to each side of the equation.
0.2854230377 + -2.242609582x + -0.2854230377 + x2 = 0 + -0.2854230377

Reorder the terms:
0.2854230377 + -0.2854230377 + -2.242609582x + x2 = 0 + -0.2854230377

Combine like terms: 0.2854230377 + -0.2854230377 = 0.0000000000
0.0000000000 + -2.242609582x + x2 = 0 + -0.2854230377
-2.242609582x + x2 = 0 + -0.2854230377

Combine like terms: 0 + -0.2854230377 = -0.2854230377
-2.242609582x + x2 = -0.2854230377

The x term is -2.242609582x.  Take half its coefficient (-1.121304791).
Square it (1.257324434) and add it to both sides.

Add '1.257324434' to each side of the equation.
-2.242609582x + 1.257324434 + x2 = -0.2854230377 + 1.257324434

Reorder the terms:
1.257324434 + -2.242609582x + x2 = -0.2854230377 + 1.257324434

Combine like terms: -0.2854230377 + 1.257324434 = 0.9719013963
1.257324434 + -2.242609582x + x2 = 0.9719013963

Factor a perfect square on the left side:
(x + -1.121304791)(x + -1.121304791) = 0.9719013963

Calculate the square root of the right side: 0.985850595

Break this problem into two subproblems by setting 
(x + -1.121304791) equal to 0.985850595 and -0.985850595.

Subproblem 1
x + -1.121304791 = 0.985850595

Simplifying
x + -1.121304791 = 0.985850595

Reorder the terms:
-1.121304791 + x = 0.985850595

Solving
-1.121304791 + x = 0.985850595

Solving for variable 'x'.

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

Add '1.121304791' to each side of the equation.
-1.121304791 + 1.121304791 + x = 0.985850595 + 1.121304791

Combine like terms: -1.121304791 + 1.121304791 = 0.000000000
0.000000000 + x = 0.985850595 + 1.121304791
x = 0.985850595 + 1.121304791

Combine like terms: 0.985850595 + 1.121304791 = 2.107155386
x = 2.107155386

Simplifying
x = 2.107155386

Subproblem 2
x + -1.121304791 = -0.985850595

Simplifying
x + -1.121304791 = -0.985850595

Reorder the terms:
-1.121304791 + x = -0.985850595

Solving
-1.121304791 + x = -0.985850595

Solving for variable 'x'.

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

Add '1.121304791' to each side of the equation.
-1.121304791 + 1.121304791 + x = -0.985850595 + 1.121304791

Combine like terms: -1.121304791 + 1.121304791 = 0.000000000
0.000000000 + x = -0.985850595 + 1.121304791
x = -0.985850595 + 1.121304791

Combine like terms: -0.985850595 + 1.121304791 = 0.135454196
x = 0.135454196

Simplifying
x = 0.135454196

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.107155386, 0.135454196}