3x^2-18x+5x=47

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Solution for 3x^2-18x+5x=47 equation: 


Simplifying
3x2 + -18x + 5x = 47

Reorder the terms:
-18x + 5x + 3x2 = 47

Combine like terms: -18x + 5x = -13x
-13x + 3x2 = 47

Solving
-13x + 3x2 = 47

Solving for variable 'x'.

Reorder the terms:
-47 + -13x + 3x2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + -13x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-15.66666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '15.66666667' to each side of the equation.
-15.66666667 + -4.333333333x + 15.66666667 + x2 = 0 + 15.66666667

Reorder the terms:
-15.66666667 + 15.66666667 + -4.333333333x + x2 = 0 + 15.66666667

Combine like terms: -15.66666667 + 15.66666667 = 0.00000000
0.00000000 + -4.333333333x + x2 = 0 + 15.66666667
-4.333333333x + x2 = 0 + 15.66666667

Combine like terms: 0 + 15.66666667 = 15.66666667
-4.333333333x + x2 = 15.66666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 15.66666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 15.66666667 + 4.694444446

Combine like terms: 15.66666667 + 4.694444446 = 20.361111116
4.694444446 + -4.333333333x + x2 = 20.361111116

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 20.361111116

Calculate the square root of the right side: 4.512328791

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 4.512328791 and -4.512328791.


Subproblem 1
x + -2.166666667 = 4.512328791

Simplifying
x + -2.166666667 = 4.512328791

Reorder the terms:
-2.166666667 + x = 4.512328791

Solving
-2.166666667 + x = 4.512328791

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 4.512328791 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 4.512328791 + 2.166666667
x = 4.512328791 + 2.166666667

Combine like terms: 4.512328791 + 2.166666667 = 6.678995458
x = 6.678995458

Simplifying
x = 6.678995458


Subproblem 2
x + -2.166666667 = -4.512328791

Simplifying
x + -2.166666667 = -4.512328791

Reorder the terms:
-2.166666667 + x = -4.512328791

Solving
-2.166666667 + x = -4.512328791

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -4.512328791 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -4.512328791 + 2.166666667
x = -4.512328791 + 2.166666667

Combine like terms: -4.512328791 + 2.166666667 = -2.345662124
x = -2.345662124

Simplifying
x = -2.345662124


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.678995458, -2.345662124}

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