3x^2-x=162

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Solution for 3x^2-x=162 equation: 


Simplifying
3x2 + -1x = 162

Reorder the terms:
-1x + 3x2 = 162

Solving
-1x + 3x2 = 162

Solving for variable 'x'.

Reorder the terms:
-162 + -1x + 3x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + -1x + 3x2 = 0

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

Divide each side by '3'.
-54 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -0.3333333333x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -0.3333333333x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -0.3333333333x + x2 = 0 + 54
-0.3333333333x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-0.3333333333x + x2 = 54

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 54 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 54 + 0.02777777779

Combine like terms: 54 + 0.02777777779 = 54.02777777779
0.02777777779 + -0.3333333333x + x2 = 54.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 54.02777777779

Calculate the square root of the right side: 7.350359024

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 7.350359024 and -7.350359024.


Subproblem 1
x + -0.1666666667 = 7.350359024

Simplifying
x + -0.1666666667 = 7.350359024

Reorder the terms:
-0.1666666667 + x = 7.350359024

Solving
-0.1666666667 + x = 7.350359024

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 7.350359024 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 7.350359024 + 0.1666666667
x = 7.350359024 + 0.1666666667

Combine like terms: 7.350359024 + 0.1666666667 = 7.5170256907
x = 7.5170256907

Simplifying
x = 7.5170256907


Subproblem 2
x + -0.1666666667 = -7.350359024

Simplifying
x + -0.1666666667 = -7.350359024

Reorder the terms:
-0.1666666667 + x = -7.350359024

Solving
-0.1666666667 + x = -7.350359024

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -7.350359024 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -7.350359024 + 0.1666666667
x = -7.350359024 + 0.1666666667

Combine like terms: -7.350359024 + 0.1666666667 = -7.1836923573
x = -7.1836923573

Simplifying
x = -7.1836923573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.5170256907, -7.1836923573}

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