4x^2-6x-55=0

Solution for 4x^2-6x-55=0 equation:

Simplifying
4x2 + -6x + -55 = 0

Reorder the terms:
-55 + -6x + 4x2 = 0

Solving
-55 + -6x + 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'.
-13.75 + -1.5x + x2 = 0

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + -1.5x + 13.75 + x2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + -1.5x + x2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + -1.5x + x2 = 0 + 13.75
-1.5x + x2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
-1.5x + x2 = 13.75

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 13.75 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 13.75 + 0.5625

Combine like terms: 13.75 + 0.5625 = 14.3125
0.5625 + -1.5x + x2 = 14.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 14.3125

Calculate the square root of the right side: 3.783186488

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.783186488 and -3.783186488.

Subproblem 1
x + -0.75 = 3.783186488

Simplifying
x + -0.75 = 3.783186488

Reorder the terms:
-0.75 + x = 3.783186488

Solving
-0.75 + x = 3.783186488

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 3.783186488 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.783186488 + 0.75
x = 3.783186488 + 0.75

Combine like terms: 3.783186488 + 0.75 = 4.533186488
x = 4.533186488

Simplifying
x = 4.533186488

Subproblem 2
x + -0.75 = -3.783186488

Simplifying
x + -0.75 = -3.783186488

Reorder the terms:
-0.75 + x = -3.783186488

Solving
-0.75 + x = -3.783186488

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -3.783186488 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.783186488 + 0.75
x = -3.783186488 + 0.75

Combine like terms: -3.783186488 + 0.75 = -3.033186488
x = -3.033186488

Simplifying
x = -3.033186488

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.533186488, -3.033186488}