4x^2-11x+4=0

Solution for 4x^2-11x+4=0 equation:

Simplifying
4x2 + -11x + 4 = 0

Reorder the terms:
4 + -11x + 4x2 = 0

Solving
4 + -11x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1 + -2.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -2.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.75x + x2 = 0 + -1
-2.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.75x + x2 = -1

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = -1 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = -1 + 1.890625

Combine like terms: -1 + 1.890625 = 0.890625
1.890625 + -2.75x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -1.375) equal to 0.943729304 and -0.943729304.

Subproblem 1
x + -1.375 = 0.943729304

Simplifying
x + -1.375 = 0.943729304

Reorder the terms:
-1.375 + x = 0.943729304

Solving
-1.375 + x = 0.943729304

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = 0.943729304 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = 0.943729304 + 1.375
x = 0.943729304 + 1.375

Combine like terms: 0.943729304 + 1.375 = 2.318729304
x = 2.318729304

Simplifying
x = 2.318729304

Subproblem 2
x + -1.375 = -0.943729304

Simplifying
x + -1.375 = -0.943729304

Reorder the terms:
-1.375 + x = -0.943729304

Solving
-1.375 + x = -0.943729304

Solving for variable 'x'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + x = -0.943729304 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = -0.943729304 + 1.375
x = -0.943729304 + 1.375

Combine like terms: -0.943729304 + 1.375 = 0.431270696
x = 0.431270696

Simplifying
x = 0.431270696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.318729304, 0.431270696}