110=(x+5)(2x)

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Solution for 110=(x+5)(2x) equation:


Simplifying
110 = (x + 5)(2x)

Reorder the terms:
110 = (5 + x)(2x)

Remove parenthesis around (2x)
110 = (5 + x) * 2x

Reorder the terms for easier multiplication:
110 = 2x(5 + x)
110 = (5 * 2x + x * 2x)
110 = (10x + 2x2)

Solving
110 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
110 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
110 + -10x + -2x2 = 0 + 2x2 + -2x2
110 + -10x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
110 + -10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(55 + -5x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(55 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
55 + -5x + -1x2 = 0

Solving
55 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-55 + 5x + x2 = 0

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 5x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 5x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 5x + x2 = 0 + 55
5x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
5x + x2 = 55

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 55 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 55 + 6.25

Combine like terms: 55 + 6.25 = 61.25
6.25 + 5x + x2 = 61.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 61.25

Calculate the square root of the right side: 7.826237921

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.826237921 and -7.826237921.


Subproblem 1
x + 2.5 = 7.826237921

Simplifying
x + 2.5 = 7.826237921

Reorder the terms:
2.5 + x = 7.826237921

Solving
2.5 + x = 7.826237921

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 7.826237921 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.826237921 + -2.5
x = 7.826237921 + -2.5

Combine like terms: 7.826237921 + -2.5 = 5.326237921
x = 5.326237921

Simplifying
x = 5.326237921


Subproblem 2
x + 2.5 = -7.826237921

Simplifying
x + 2.5 = -7.826237921

Reorder the terms:
2.5 + x = -7.826237921

Solving
2.5 + x = -7.826237921

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -7.826237921 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.826237921 + -2.5
x = -7.826237921 + -2.5

Combine like terms: -7.826237921 + -2.5 = -10.326237921
x = -10.326237921

Simplifying
x = -10.326237921


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.326237921, -10.326237921}
Solution
x = {5.326237921, -10.326237921}

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