9x^2-48x-28=0

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Solution for 9x^2-48x-28=0 equation: 


Simplifying
9x2 + -48x + -28 = 0

Reorder the terms:
-28 + -48x + 9x2 = 0

Solving
-28 + -48x + 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 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '3.111111111' to each side of the equation.
-3.111111111 + -5.333333333x + 3.111111111 + x2 = 0 + 3.111111111

Reorder the terms:
-3.111111111 + 3.111111111 + -5.333333333x + x2 = 0 + 3.111111111

Combine like terms: -3.111111111 + 3.111111111 = 0.000000000
0.000000000 + -5.333333333x + x2 = 0 + 3.111111111
-5.333333333x + x2 = 0 + 3.111111111

Combine like terms: 0 + 3.111111111 = 3.111111111
-5.333333333x + x2 = 3.111111111

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 3.111111111 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 3.111111111 + 7.111111113

Combine like terms: 3.111111111 + 7.111111113 = 10.222222224
7.111111113 + -5.333333333x + x2 = 10.222222224

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 10.222222224

Calculate the square root of the right side: 3.197221016

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 3.197221016 and -3.197221016.


Subproblem 1
x + -2.666666667 = 3.197221016

Simplifying
x + -2.666666667 = 3.197221016

Reorder the terms:
-2.666666667 + x = 3.197221016

Solving
-2.666666667 + x = 3.197221016

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 3.197221016 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 3.197221016 + 2.666666667
x = 3.197221016 + 2.666666667

Combine like terms: 3.197221016 + 2.666666667 = 5.863887683
x = 5.863887683

Simplifying
x = 5.863887683


Subproblem 2
x + -2.666666667 = -3.197221016

Simplifying
x + -2.666666667 = -3.197221016

Reorder the terms:
-2.666666667 + x = -3.197221016

Solving
-2.666666667 + x = -3.197221016

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -3.197221016 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -3.197221016 + 2.666666667
x = -3.197221016 + 2.666666667

Combine like terms: -3.197221016 + 2.666666667 = -0.530554349
x = -0.530554349

Simplifying
x = -0.530554349


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.863887683, -0.530554349}

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