(2x)(x+10)+110=360

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Solution for (2x)(x+10)+110=360 equation: 


Simplifying
(2x)(x + 10) + 110 = 360

Remove parenthesis around (2x)
2x(x + 10) + 110 = 360

Reorder the terms:
2x(10 + x) + 110 = 360
(10 * 2x + x * 2x) + 110 = 360
(20x + 2x2) + 110 = 360

Reorder the terms:
110 + 20x + 2x2 = 360

Solving
110 + 20x + 2x2 = 360

Solving for variable 'x'.

Reorder the terms:
110 + -360 + 20x + 2x2 = 360 + -360

Combine like terms: 110 + -360 = -250
-250 + 20x + 2x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-250 + 20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-125 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-125 + 10x + x2 = 0

Solving
-125 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + 10x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + 10x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 10x + x2 = 0 + 125
10x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
10x + x2 = 125

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 = 125 + 25

Reorder the terms:
25 + 10x + x2 = 125 + 25

Combine like terms: 125 + 25 = 150
25 + 10x + x2 = 150

Factor a perfect square on the left side:
(x + 5)(x + 5) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + 5) equal to 12.247448714 and -12.247448714.


Subproblem 1
x + 5 = 12.247448714

Simplifying
x + 5 = 12.247448714

Reorder the terms:
5 + x = 12.247448714

Solving
5 + x = 12.247448714

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 = 12.247448714 + -5

Combine like terms: 5 + -5 = 0
0 + x = 12.247448714 + -5
x = 12.247448714 + -5

Combine like terms: 12.247448714 + -5 = 7.247448714
x = 7.247448714

Simplifying
x = 7.247448714


Subproblem 2
x + 5 = -12.247448714

Simplifying
x + 5 = -12.247448714

Reorder the terms:
5 + x = -12.247448714

Solving
5 + x = -12.247448714

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 = -12.247448714 + -5

Combine like terms: 5 + -5 = 0
0 + x = -12.247448714 + -5
x = -12.247448714 + -5

Combine like terms: -12.247448714 + -5 = -17.247448714
x = -17.247448714

Simplifying
x = -17.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.247448714, -17.247448714}
Solution
x = {7.247448714, -17.247448714}

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