3x^2+32x-1=0

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Solution for 3x^2+32x-1=0 equation: 


Simplifying
3x2 + 32x + -1 = 0

Reorder the terms:
-1 + 32x + 3x2 = 0

Solving
-1 + 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'.
-0.3333333333 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 10.66666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 10.66666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 10.66666667x + x2 = 0 + 0.3333333333
10.66666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
10.66666667x + x2 = 0.3333333333

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 = 0.3333333333 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = 0.3333333333 + 28.44444446

Combine like terms: 0.3333333333 + 28.44444446 = 28.7777777933
28.44444446 + 10.66666667x + x2 = 28.7777777933

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 28.7777777933

Calculate the square root of the right side: 5.364492315

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 5.364492315 and -5.364492315.


Subproblem 1
x + 5.333333335 = 5.364492315

Simplifying
x + 5.333333335 = 5.364492315

Reorder the terms:
5.333333335 + x = 5.364492315

Solving
5.333333335 + x = 5.364492315

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 = 5.364492315 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 5.364492315 + -5.333333335
x = 5.364492315 + -5.333333335

Combine like terms: 5.364492315 + -5.333333335 = 0.03115898
x = 0.03115898

Simplifying
x = 0.03115898


Subproblem 2
x + 5.333333335 = -5.364492315

Simplifying
x + 5.333333335 = -5.364492315

Reorder the terms:
5.333333335 + x = -5.364492315

Solving
5.333333335 + x = -5.364492315

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 = -5.364492315 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -5.364492315 + -5.333333335
x = -5.364492315 + -5.333333335

Combine like terms: -5.364492315 + -5.333333335 = -10.69782565
x = -10.69782565

Simplifying
x = -10.69782565


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03115898, -10.69782565}

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