3x^2-28x-9=0

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Solution for 3x^2-28x-9=0 equation: 


Simplifying
3x2 + -28x + -9 = 0

Reorder the terms:
-9 + -28x + 3x2 = 0

Solving
-9 + -28x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -9.333333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -9.333333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -9.333333333x + x2 = 0 + 3
-9.333333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-9.333333333x + x2 = 3

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 3 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 3 + 21.77777778

Combine like terms: 3 + 21.77777778 = 24.77777778
21.77777778 + -9.333333333x + x2 = 24.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 24.77777778

Calculate the square root of the right side: 4.977728175

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 4.977728175 and -4.977728175.


Subproblem 1
x + -4.666666667 = 4.977728175

Simplifying
x + -4.666666667 = 4.977728175

Reorder the terms:
-4.666666667 + x = 4.977728175

Solving
-4.666666667 + x = 4.977728175

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 4.977728175 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 4.977728175 + 4.666666667
x = 4.977728175 + 4.666666667

Combine like terms: 4.977728175 + 4.666666667 = 9.644394842
x = 9.644394842

Simplifying
x = 9.644394842


Subproblem 2
x + -4.666666667 = -4.977728175

Simplifying
x + -4.666666667 = -4.977728175

Reorder the terms:
-4.666666667 + x = -4.977728175

Solving
-4.666666667 + x = -4.977728175

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -4.977728175 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -4.977728175 + 4.666666667
x = -4.977728175 + 4.666666667

Combine like terms: -4.977728175 + 4.666666667 = -0.311061508
x = -0.311061508

Simplifying
x = -0.311061508


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.644394842, -0.311061508}

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