2x(x+10)=100

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Solution for 2x(x+10)=100 equation: 


Simplifying
2x(x + 10) = 100

Reorder the terms:
2x(10 + x) = 100
(10 * 2x + x * 2x) = 100
(20x + 2x2) = 100

Solving
20x + 2x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 20x + 2x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + 10x + x2 = 0

Solving
-50 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 10x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 10x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 10x + x2 = 0 + 50
10x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
10x + x2 = 50

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 = 50 + 25

Reorder the terms:
25 + 10x + x2 = 50 + 25

Combine like terms: 50 + 25 = 75
25 + 10x + x2 = 75

Factor a perfect square on the left side:
(x + 5)(x + 5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 5) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 5 = 8.660254038

Simplifying
x + 5 = 8.660254038

Reorder the terms:
5 + x = 8.660254038

Solving
5 + x = 8.660254038

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 = 8.660254038 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.660254038 + -5
x = 8.660254038 + -5

Combine like terms: 8.660254038 + -5 = 3.660254038
x = 3.660254038

Simplifying
x = 3.660254038


Subproblem 2
x + 5 = -8.660254038

Simplifying
x + 5 = -8.660254038

Reorder the terms:
5 + x = -8.660254038

Solving
5 + x = -8.660254038

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 = -8.660254038 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.660254038 + -5
x = -8.660254038 + -5

Combine like terms: -8.660254038 + -5 = -13.660254038
x = -13.660254038

Simplifying
x = -13.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.660254038, -13.660254038}
Solution
x = {3.660254038, -13.660254038}

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