2x*(10+x)=330

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Solution for 2x*(10+x)=330 equation: 


Simplifying
2x(10 + x) = 330
(10 * 2x + x * 2x) = 330
(20x + 2x2) = 330

Solving
20x + 2x2 = 330

Solving for variable 'x'.

Reorder the terms:
-330 + 20x + 2x2 = 330 + -330

Combine like terms: 330 + -330 = 0
-330 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-165 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-165 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-165 + 10x + x2 = 0

Solving
-165 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + 10x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + 10x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + 10x + x2 = 0 + 165
10x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
10x + x2 = 165

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 165 + 25

Reorder the terms:
25 + 10x + x2 = 165 + 25

Combine like terms: 165 + 25 = 190
25 + 10x + x2 = 190

Factor a perfect square on the left side:
(x + 5)(x + 5) = 190

Calculate the square root of the right side: 13.784048752

Break this problem into two subproblems by setting 
(x + 5) equal to 13.784048752 and -13.784048752.


Subproblem 1
x + 5 = 13.784048752

Simplifying
x + 5 = 13.784048752

Reorder the terms:
5 + x = 13.784048752

Solving
5 + x = 13.784048752

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 13.784048752 + -5

Combine like terms: 5 + -5 = 0
0 + x = 13.784048752 + -5
x = 13.784048752 + -5

Combine like terms: 13.784048752 + -5 = 8.784048752
x = 8.784048752

Simplifying
x = 8.784048752


Subproblem 2
x + 5 = -13.784048752

Simplifying
x + 5 = -13.784048752

Reorder the terms:
5 + x = -13.784048752

Solving
5 + x = -13.784048752

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -13.784048752 + -5

Combine like terms: 5 + -5 = 0
0 + x = -13.784048752 + -5
x = -13.784048752 + -5

Combine like terms: -13.784048752 + -5 = -18.784048752
x = -18.784048752

Simplifying
x = -18.784048752


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.784048752, -18.784048752}
Solution
x = {8.784048752, -18.784048752}

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