-18x^2+79x-9=0

Solution for -18x^2+79x-9=0 equation:

Simplifying
-18x2 + 79x + -9 = 0

Reorder the terms:
-9 + 79x + -18x2 = 0

Solving
-9 + 79x + -18x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-18 the coefficient of the squared term: 

Divide each side by '-18'.
0.5 + -4.388888889x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4.388888889x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4.388888889x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4.388888889x + x2 = 0 + -0.5
-4.388888889x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4.388888889x + x2 = -0.5

The x term is -4.388888889x.  Take half its coefficient (-2.194444445).
Square it (4.815586422) and add it to both sides.

Add '4.815586422' to each side of the equation.
-4.388888889x + 4.815586422 + x2 = -0.5 + 4.815586422

Reorder the terms:
4.815586422 + -4.388888889x + x2 = -0.5 + 4.815586422

Combine like terms: -0.5 + 4.815586422 = 4.315586422
4.815586422 + -4.388888889x + x2 = 4.315586422

Factor a perfect square on the left side:
(x + -2.194444445)(x + -2.194444445) = 4.315586422

Calculate the square root of the right side: 2.077398956

Break this problem into two subproblems by setting 
(x + -2.194444445) equal to 2.077398956 and -2.077398956.

Subproblem 1
x + -2.194444445 = 2.077398956

Simplifying
x + -2.194444445 = 2.077398956

Reorder the terms:
-2.194444445 + x = 2.077398956

Solving
-2.194444445 + x = 2.077398956

Solving for variable 'x'.

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

Add '2.194444445' to each side of the equation.
-2.194444445 + 2.194444445 + x = 2.077398956 + 2.194444445

Combine like terms: -2.194444445 + 2.194444445 = 0.000000000
0.000000000 + x = 2.077398956 + 2.194444445
x = 2.077398956 + 2.194444445

Combine like terms: 2.077398956 + 2.194444445 = 4.271843401
x = 4.271843401

Simplifying
x = 4.271843401

Subproblem 2
x + -2.194444445 = -2.077398956

Simplifying
x + -2.194444445 = -2.077398956

Reorder the terms:
-2.194444445 + x = -2.077398956

Solving
-2.194444445 + x = -2.077398956

Solving for variable 'x'.

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

Add '2.194444445' to each side of the equation.
-2.194444445 + 2.194444445 + x = -2.077398956 + 2.194444445

Combine like terms: -2.194444445 + 2.194444445 = 0.000000000
0.000000000 + x = -2.077398956 + 2.194444445
x = -2.077398956 + 2.194444445

Combine like terms: -2.077398956 + 2.194444445 = 0.117045489
x = 0.117045489

Simplifying
x = 0.117045489

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.271843401, 0.117045489}