3x^2+47x-230=0

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Solution for 3x^2+47x-230=0 equation: 


Simplifying
3x2 + 47x + -230 = 0

Reorder the terms:
-230 + 47x + 3x2 = 0

Solving
-230 + 47x + 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'.
-76.66666667 + 15.66666667x + x2 = 0

Move the constant term to the right:

Add '76.66666667' to each side of the equation.
-76.66666667 + 15.66666667x + 76.66666667 + x2 = 0 + 76.66666667

Reorder the terms:
-76.66666667 + 76.66666667 + 15.66666667x + x2 = 0 + 76.66666667

Combine like terms: -76.66666667 + 76.66666667 = 0.00000000
0.00000000 + 15.66666667x + x2 = 0 + 76.66666667
15.66666667x + x2 = 0 + 76.66666667

Combine like terms: 0 + 76.66666667 = 76.66666667
15.66666667x + x2 = 76.66666667

The x term is 15.66666667x.  Take half its coefficient (7.833333335).
Square it (61.36111114) and add it to both sides.

Add '61.36111114' to each side of the equation.
15.66666667x + 61.36111114 + x2 = 76.66666667 + 61.36111114

Reorder the terms:
61.36111114 + 15.66666667x + x2 = 76.66666667 + 61.36111114

Combine like terms: 76.66666667 + 61.36111114 = 138.02777781
61.36111114 + 15.66666667x + x2 = 138.02777781

Factor a perfect square on the left side:
(x + 7.833333335)(x + 7.833333335) = 138.02777781

Calculate the square root of the right side: 11.748522367

Break this problem into two subproblems by setting 
(x + 7.833333335) equal to 11.748522367 and -11.748522367.


Subproblem 1
x + 7.833333335 = 11.748522367

Simplifying
x + 7.833333335 = 11.748522367

Reorder the terms:
7.833333335 + x = 11.748522367

Solving
7.833333335 + x = 11.748522367

Solving for variable 'x'.

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

Add '-7.833333335' to each side of the equation.
7.833333335 + -7.833333335 + x = 11.748522367 + -7.833333335

Combine like terms: 7.833333335 + -7.833333335 = 0.000000000
0.000000000 + x = 11.748522367 + -7.833333335
x = 11.748522367 + -7.833333335

Combine like terms: 11.748522367 + -7.833333335 = 3.915189032
x = 3.915189032

Simplifying
x = 3.915189032


Subproblem 2
x + 7.833333335 = -11.748522367

Simplifying
x + 7.833333335 = -11.748522367

Reorder the terms:
7.833333335 + x = -11.748522367

Solving
7.833333335 + x = -11.748522367

Solving for variable 'x'.

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

Add '-7.833333335' to each side of the equation.
7.833333335 + -7.833333335 + x = -11.748522367 + -7.833333335

Combine like terms: 7.833333335 + -7.833333335 = 0.000000000
0.000000000 + x = -11.748522367 + -7.833333335
x = -11.748522367 + -7.833333335

Combine like terms: -11.748522367 + -7.833333335 = -19.581855702
x = -19.581855702

Simplifying
x = -19.581855702


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.915189032, -19.581855702}

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