4x^2-10x-9=0

Solution for 4x^2-10x-9=0 equation:

Simplifying
4x2 + -10x + -9 = 0

Reorder the terms:
-9 + -10x + 4x2 = 0

Solving
-9 + -10x + 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'.
-2.25 + -2.5x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -2.5x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -2.5x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -2.5x + x2 = 0 + 2.25
-2.5x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-2.5x + x2 = 2.25

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 2.25 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 2.25 + 1.5625

Combine like terms: 2.25 + 1.5625 = 3.8125
1.5625 + -2.5x + x2 = 3.8125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.952562419 and -1.952562419.

Subproblem 1
x + -1.25 = 1.952562419

Simplifying
x + -1.25 = 1.952562419

Reorder the terms:
-1.25 + x = 1.952562419

Solving
-1.25 + x = 1.952562419

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.952562419 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.952562419 + 1.25
x = 1.952562419 + 1.25

Combine like terms: 1.952562419 + 1.25 = 3.202562419
x = 3.202562419

Simplifying
x = 3.202562419

Subproblem 2
x + -1.25 = -1.952562419

Simplifying
x + -1.25 = -1.952562419

Reorder the terms:
-1.25 + x = -1.952562419

Solving
-1.25 + x = -1.952562419

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.952562419 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.952562419 + 1.25
x = -1.952562419 + 1.25

Combine like terms: -1.952562419 + 1.25 = -0.702562419
x = -0.702562419

Simplifying
x = -0.702562419

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.202562419, -0.702562419}