9x^2-4.5x-3.5=0

Solution for 9x^2-4.5x-3.5=0 equation:

Simplifying
9x2 + -4.5x + -3.5 = 0

Reorder the terms:
-3.5 + -4.5x + 9x2 = 0

Solving
-3.5 + -4.5x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.3888888889 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.3888888889' to each side of the equation.
-0.3888888889 + -0.5x + 0.3888888889 + x2 = 0 + 0.3888888889

Reorder the terms:
-0.3888888889 + 0.3888888889 + -0.5x + x2 = 0 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + 0.3888888889
-0.5x + x2 = 0 + 0.3888888889

Combine like terms: 0 + 0.3888888889 = 0.3888888889
-0.5x + x2 = 0.3888888889

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.3888888889 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.3888888889 + 0.0625

Combine like terms: 0.3888888889 + 0.0625 = 0.4513888889
0.0625 + -0.5x + x2 = 0.4513888889

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.4513888889

Calculate the square root of the right side: 0.671854812

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.671854812 and -0.671854812.

Subproblem 1
x + -0.25 = 0.671854812

Simplifying
x + -0.25 = 0.671854812

Reorder the terms:
-0.25 + x = 0.671854812

Solving
-0.25 + x = 0.671854812

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.671854812 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.671854812 + 0.25
x = 0.671854812 + 0.25

Combine like terms: 0.671854812 + 0.25 = 0.921854812
x = 0.921854812

Simplifying
x = 0.921854812

Subproblem 2
x + -0.25 = -0.671854812

Simplifying
x + -0.25 = -0.671854812

Reorder the terms:
-0.25 + x = -0.671854812

Solving
-0.25 + x = -0.671854812

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.671854812 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.671854812 + 0.25
x = -0.671854812 + 0.25

Combine like terms: -0.671854812 + 0.25 = -0.421854812
x = -0.421854812

Simplifying
x = -0.421854812

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.921854812, -0.421854812}