2x+x(3x-18)=180

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Solution for 2x+x(3x-18)=180 equation:


Simplifying
2x + x(3x + -18) = 180

Reorder the terms:
2x + x(-18 + 3x) = 180
2x + (-18 * x + 3x * x) = 180
2x + (-18x + 3x2) = 180

Combine like terms: 2x + -18x = -16x
-16x + 3x2 = 180

Solving
-16x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -16x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -16x + 3x2 = 0

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

Divide each side by '3'.
-60 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -5.333333333x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -5.333333333x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -5.333333333x + x2 = 0 + 60
-5.333333333x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-5.333333333x + x2 = 60

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 60 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 60 + 7.111111113

Combine like terms: 60 + 7.111111113 = 67.111111113
7.111111113 + -5.333333333x + x2 = 67.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 67.111111113

Calculate the square root of the right side: 8.192137152

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 8.192137152 and -8.192137152.


Subproblem 1
x + -2.666666667 = 8.192137152

Simplifying
x + -2.666666667 = 8.192137152

Reorder the terms:
-2.666666667 + x = 8.192137152

Solving
-2.666666667 + x = 8.192137152

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 8.192137152 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 8.192137152 + 2.666666667
x = 8.192137152 + 2.666666667

Combine like terms: 8.192137152 + 2.666666667 = 10.858803819
x = 10.858803819

Simplifying
x = 10.858803819


Subproblem 2
x + -2.666666667 = -8.192137152

Simplifying
x + -2.666666667 = -8.192137152

Reorder the terms:
-2.666666667 + x = -8.192137152

Solving
-2.666666667 + x = -8.192137152

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -8.192137152 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -8.192137152 + 2.666666667
x = -8.192137152 + 2.666666667

Combine like terms: -8.192137152 + 2.666666667 = -5.525470485
x = -5.525470485

Simplifying
x = -5.525470485


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.858803819, -5.525470485}

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