-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 = 2.890625
1.890625 + -2.75x + x2 = 2.890625

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(x + -1.375) equal to 1.700183814 and -1.700183814.

Subproblem 1
x + -1.375 = 1.700183814

Simplifying
x + -1.375 = 1.700183814

Reorder the terms:
-1.375 + x = 1.700183814

Solving
-1.375 + x = 1.700183814

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 = 1.700183814 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = 1.700183814 + 1.375
x = 1.700183814 + 1.375

Combine like terms: 1.700183814 + 1.375 = 3.075183814
x = 3.075183814

Simplifying
x = 3.075183814

Subproblem 2
x + -1.375 = -1.700183814

Simplifying
x + -1.375 = -1.700183814

Reorder the terms:
-1.375 + x = -1.700183814

Solving
-1.375 + x = -1.700183814

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 = -1.700183814 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + x = -1.700183814 + 1.375
x = -1.700183814 + 1.375

Combine like terms: -1.700183814 + 1.375 = -0.325183814
x = -0.325183814

Simplifying
x = -0.325183814

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.075183814, -0.325183814}