2X(X+10)=220

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Solution for 2X(X+10)=220 equation: 


Simplifying
2X(X + 10) = 220

Reorder the terms:
2X(10 + X) = 220
(10 * 2X + X * 2X) = 220
(20X + 2X2) = 220

Solving
20X + 2X2 = 220

Solving for variable 'X'.

Reorder the terms:
-220 + 20X + 2X2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + 20X + 2X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-110 + 10X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-110 + 10X + X2)' equal to zero and attempt to solve:

Simplifying
-110 + 10X + X2 = 0

Solving
-110 + 10X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 10X + 110 + X2 = 0 + 110

Reorder the terms:
-110 + 110 + 10X + X2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 10X + X2 = 0 + 110
10X + X2 = 0 + 110

Combine like terms: 0 + 110 = 110
10X + X2 = 110

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 = 110 + 25

Reorder the terms:
25 + 10X + X2 = 110 + 25

Combine like terms: 110 + 25 = 135
25 + 10X + X2 = 135

Factor a perfect square on the left side:
(X + 5)(X + 5) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(X + 5) equal to 11.618950039 and -11.618950039.


Subproblem 1
X + 5 = 11.618950039

Simplifying
X + 5 = 11.618950039

Reorder the terms:
5 + X = 11.618950039

Solving
5 + X = 11.618950039

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 = 11.618950039 + -5

Combine like terms: 5 + -5 = 0
0 + X = 11.618950039 + -5
X = 11.618950039 + -5

Combine like terms: 11.618950039 + -5 = 6.618950039
X = 6.618950039

Simplifying
X = 6.618950039


Subproblem 2
X + 5 = -11.618950039

Simplifying
X + 5 = -11.618950039

Reorder the terms:
5 + X = -11.618950039

Solving
5 + X = -11.618950039

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 = -11.618950039 + -5

Combine like terms: 5 + -5 = 0
0 + X = -11.618950039 + -5
X = -11.618950039 + -5

Combine like terms: -11.618950039 + -5 = -16.618950039
X = -16.618950039

Simplifying
X = -16.618950039


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.618950039, -16.618950039}
Solution
X = {6.618950039, -16.618950039}

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