3x^2-32x-19=0

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Solution for 3x^2-32x-19=0 equation: 


Simplifying
3x2 + -32x + -19 = 0

Reorder the terms:
-19 + -32x + 3x2 = 0

Solving
-19 + -32x + 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'.
-6.333333333 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + -10.66666667x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + -10.66666667x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + -10.66666667x + x2 = 0 + 6.333333333
-10.66666667x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
-10.66666667x + x2 = 6.333333333

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = 6.333333333 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = 6.333333333 + 28.44444446

Combine like terms: 6.333333333 + 28.44444446 = 34.777777793
28.44444446 + -10.66666667x + x2 = 34.777777793

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 34.777777793

Calculate the square root of the right side: 5.897268672

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 5.897268672 and -5.897268672.


Subproblem 1
x + -5.333333335 = 5.897268672

Simplifying
x + -5.333333335 = 5.897268672

Reorder the terms:
-5.333333335 + x = 5.897268672

Solving
-5.333333335 + x = 5.897268672

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 5.897268672 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 5.897268672 + 5.333333335
x = 5.897268672 + 5.333333335

Combine like terms: 5.897268672 + 5.333333335 = 11.230602007
x = 11.230602007

Simplifying
x = 11.230602007


Subproblem 2
x + -5.333333335 = -5.897268672

Simplifying
x + -5.333333335 = -5.897268672

Reorder the terms:
-5.333333335 + x = -5.897268672

Solving
-5.333333335 + x = -5.897268672

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -5.897268672 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -5.897268672 + 5.333333335
x = -5.897268672 + 5.333333335

Combine like terms: -5.897268672 + 5.333333335 = -0.563935337
x = -0.563935337

Simplifying
x = -0.563935337


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.230602007, -0.563935337}

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