4.5x^2-3.7x-7.4=0

Solution for 4.5x^2-3.7x-7.4=0 equation:

Simplifying
4.5x2 + -3.7x + -7.4 = 0

Reorder the terms:
-7.4 + -3.7x + 4.5x2 = 0

Solving
-7.4 + -3.7x + 4.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.5'.
-1.644444444 + -0.8222222222x + x2 = 0

Move the constant term to the right:

Add '1.644444444' to each side of the equation.
-1.644444444 + -0.8222222222x + 1.644444444 + x2 = 0 + 1.644444444

Reorder the terms:
-1.644444444 + 1.644444444 + -0.8222222222x + x2 = 0 + 1.644444444

Combine like terms: -1.644444444 + 1.644444444 = 0.000000000
0.000000000 + -0.8222222222x + x2 = 0 + 1.644444444
-0.8222222222x + x2 = 0 + 1.644444444

Combine like terms: 0 + 1.644444444 = 1.644444444
-0.8222222222x + x2 = 1.644444444

The x term is -0.8222222222x.  Take half its coefficient (-0.4111111111).
Square it (0.1690123457) and add it to both sides.

Add '0.1690123457' to each side of the equation.
-0.8222222222x + 0.1690123457 + x2 = 1.644444444 + 0.1690123457

Reorder the terms:
0.1690123457 + -0.8222222222x + x2 = 1.644444444 + 0.1690123457

Combine like terms: 1.644444444 + 0.1690123457 = 1.8134567897
0.1690123457 + -0.8222222222x + x2 = 1.8134567897

Factor a perfect square on the left side:
(x + -0.4111111111)(x + -0.4111111111) = 1.8134567897

Calculate the square root of the right side: 1.346646498

Break this problem into two subproblems by setting 
(x + -0.4111111111) equal to 1.346646498 and -1.346646498.

Subproblem 1
x + -0.4111111111 = 1.346646498

Simplifying
x + -0.4111111111 = 1.346646498

Reorder the terms:
-0.4111111111 + x = 1.346646498

Solving
-0.4111111111 + x = 1.346646498

Solving for variable 'x'.

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

Add '0.4111111111' to each side of the equation.
-0.4111111111 + 0.4111111111 + x = 1.346646498 + 0.4111111111

Combine like terms: -0.4111111111 + 0.4111111111 = 0.0000000000
0.0000000000 + x = 1.346646498 + 0.4111111111
x = 1.346646498 + 0.4111111111

Combine like terms: 1.346646498 + 0.4111111111 = 1.7577576091
x = 1.7577576091

Simplifying
x = 1.7577576091

Subproblem 2
x + -0.4111111111 = -1.346646498

Simplifying
x + -0.4111111111 = -1.346646498

Reorder the terms:
-0.4111111111 + x = -1.346646498

Solving
-0.4111111111 + x = -1.346646498

Solving for variable 'x'.

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

Add '0.4111111111' to each side of the equation.
-0.4111111111 + 0.4111111111 + x = -1.346646498 + 0.4111111111

Combine like terms: -0.4111111111 + 0.4111111111 = 0.0000000000
0.0000000000 + x = -1.346646498 + 0.4111111111
x = -1.346646498 + 0.4111111111

Combine like terms: -1.346646498 + 0.4111111111 = -0.9355353869
x = -0.9355353869

Simplifying
x = -0.9355353869

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7577576091, -0.9355353869}