9x^2-28x-28=0

Solution for 9x^2-28x-28=0 equation:

Simplifying
9x2 + -28x + -28 = 0

Reorder the terms:
-28 + -28x + 9x2 = 0

Solving
-28 + -28x + 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'.
-3.111111111 + -3.111111111x + x2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + -3.111111111x + 3.111111111 + x2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + -3.111111111x + x2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + -3.111111111x + x2 = 0 + 3.111111111
-3.111111111x + x2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
-3.111111111x + x2 = 3.111111111

The x term is -3.111111111x.  Take half its coefficient (-1.555555556).
Square it (2.419753088) and add it to both sides.

Add '2.419753088' to each side of the equation.
-3.111111111x + 2.419753088 + x2 = 3.111111111 + 2.419753088

Reorder the terms:
2.419753088 + -3.111111111x + x2 = 3.111111111 + 2.419753088

Combine like terms: 3.111111111 + 2.419753088 = 5.530864199
2.419753088 + -3.111111111x + x2 = 5.530864199

Factor a perfect square on the left side:
(x + -1.555555556)(x + -1.555555556) = 5.530864199

Calculate the square root of the right side: 2.351778943

Break this problem into two subproblems by setting 
(x + -1.555555556) equal to 2.351778943 and -2.351778943.

Subproblem 1
x + -1.555555556 = 2.351778943

Simplifying
x + -1.555555556 = 2.351778943

Reorder the terms:
-1.555555556 + x = 2.351778943

Solving
-1.555555556 + x = 2.351778943

Solving for variable 'x'.

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

Add '1.555555556' to each side of the equation.
-1.555555556 + 1.555555556 + x = 2.351778943 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + x = 2.351778943 + 1.555555556
x = 2.351778943 + 1.555555556

Combine like terms: 2.351778943 + 1.555555556 = 3.907334499
x = 3.907334499

Simplifying
x = 3.907334499

Subproblem 2
x + -1.555555556 = -2.351778943

Simplifying
x + -1.555555556 = -2.351778943

Reorder the terms:
-1.555555556 + x = -2.351778943

Solving
-1.555555556 + x = -2.351778943

Solving for variable 'x'.

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

Add '1.555555556' to each side of the equation.
-1.555555556 + 1.555555556 + x = -2.351778943 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + x = -2.351778943 + 1.555555556
x = -2.351778943 + 1.555555556

Combine like terms: -2.351778943 + 1.555555556 = -0.796223387
x = -0.796223387

Simplifying
x = -0.796223387

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.907334499, -0.796223387}