3x^2+32x-47=0

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Solution for 3x^2+32x-47=0 equation: 


Simplifying
3x2 + 32x + -47 = 0

Reorder the terms:
-47 + 32x + 3x2 = 0

Solving
-47 + 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'.
-15.66666667 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '15.66666667' to each side of the equation.
-15.66666667 + 10.66666667x + 15.66666667 + x2 = 0 + 15.66666667

Reorder the terms:
-15.66666667 + 15.66666667 + 10.66666667x + x2 = 0 + 15.66666667

Combine like terms: -15.66666667 + 15.66666667 = 0.00000000
0.00000000 + 10.66666667x + x2 = 0 + 15.66666667
10.66666667x + x2 = 0 + 15.66666667

Combine like terms: 0 + 15.66666667 = 15.66666667
10.66666667x + x2 = 15.66666667

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 = 15.66666667 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = 15.66666667 + 28.44444446

Combine like terms: 15.66666667 + 28.44444446 = 44.11111113
28.44444446 + 10.66666667x + x2 = 44.11111113

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 44.11111113

Calculate the square root of the right side: 6.641619616

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 6.641619616 and -6.641619616.


Subproblem 1
x + 5.333333335 = 6.641619616

Simplifying
x + 5.333333335 = 6.641619616

Reorder the terms:
5.333333335 + x = 6.641619616

Solving
5.333333335 + x = 6.641619616

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 = 6.641619616 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 6.641619616 + -5.333333335
x = 6.641619616 + -5.333333335

Combine like terms: 6.641619616 + -5.333333335 = 1.308286281
x = 1.308286281

Simplifying
x = 1.308286281


Subproblem 2
x + 5.333333335 = -6.641619616

Simplifying
x + 5.333333335 = -6.641619616

Reorder the terms:
5.333333335 + x = -6.641619616

Solving
5.333333335 + x = -6.641619616

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 = -6.641619616 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -6.641619616 + -5.333333335
x = -6.641619616 + -5.333333335

Combine like terms: -6.641619616 + -5.333333335 = -11.974952951
x = -11.974952951

Simplifying
x = -11.974952951


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.308286281, -11.974952951}

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