4x^2-18x-5=0

Solution for 4x^2-18x-5=0 equation:

Simplifying
4x2 + -18x + -5 = 0

Reorder the terms:
-5 + -18x + 4x2 = 0

Solving
-5 + -18x + 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'.
-1.25 + -4.5x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -4.5x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -4.5x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -4.5x + x2 = 0 + 1.25
-4.5x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-4.5x + x2 = 1.25

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1.25 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1.25 + 5.0625

Combine like terms: 1.25 + 5.0625 = 6.3125
5.0625 + -4.5x + x2 = 6.3125

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.3125

Calculate the square root of the right side: 2.512468905

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.512468905 and -2.512468905.

Subproblem 1
x + -2.25 = 2.512468905

Simplifying
x + -2.25 = 2.512468905

Reorder the terms:
-2.25 + x = 2.512468905

Solving
-2.25 + x = 2.512468905

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.512468905 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.512468905 + 2.25
x = 2.512468905 + 2.25

Combine like terms: 2.512468905 + 2.25 = 4.762468905
x = 4.762468905

Simplifying
x = 4.762468905

Subproblem 2
x + -2.25 = -2.512468905

Simplifying
x + -2.25 = -2.512468905

Reorder the terms:
-2.25 + x = -2.512468905

Solving
-2.25 + x = -2.512468905

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.512468905 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.512468905 + 2.25
x = -2.512468905 + 2.25

Combine like terms: -2.512468905 + 2.25 = -0.262468905
x = -0.262468905

Simplifying
x = -0.262468905

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.762468905, -0.262468905}