3x^2+28x-6=0

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Solution for 3x^2+28x-6=0 equation: 


Simplifying
3x2 + 28x + -6 = 0

Reorder the terms:
-6 + 28x + 3x2 = 0

Solving
-6 + 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'.
-2 + 9.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 9.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 9.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9.333333333x + x2 = 0 + 2
9.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
9.333333333x + x2 = 2

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 = 2 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333x + x2 = 2 + 21.77777778

Combine like terms: 2 + 21.77777778 = 23.77777778
21.77777778 + 9.333333333x + x2 = 23.77777778

Factor a perfect square on the left side:
(x + 4.666666667)(x + 4.666666667) = 23.77777778

Calculate the square root of the right side: 4.87624628

Break this problem into two subproblems by setting 
(x + 4.666666667) equal to 4.87624628 and -4.87624628.


Subproblem 1
x + 4.666666667 = 4.87624628

Simplifying
x + 4.666666667 = 4.87624628

Reorder the terms:
4.666666667 + x = 4.87624628

Solving
4.666666667 + x = 4.87624628

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 = 4.87624628 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = 4.87624628 + -4.666666667
x = 4.87624628 + -4.666666667

Combine like terms: 4.87624628 + -4.666666667 = 0.209579613
x = 0.209579613

Simplifying
x = 0.209579613


Subproblem 2
x + 4.666666667 = -4.87624628

Simplifying
x + 4.666666667 = -4.87624628

Reorder the terms:
4.666666667 + x = -4.87624628

Solving
4.666666667 + x = -4.87624628

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 = -4.87624628 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x = -4.87624628 + -4.666666667
x = -4.87624628 + -4.666666667

Combine like terms: -4.87624628 + -4.666666667 = -9.542912947
x = -9.542912947

Simplifying
x = -9.542912947


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.209579613, -9.542912947}

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