(2X+30)(2X-20)-1100=0

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Solution for (2X+30)(2X-20)-1100=0 equation: 


Simplifying
(2X + 30)(2X + -20) + -1100 = 0

Reorder the terms:
(30 + 2X)(2X + -20) + -1100 = 0

Reorder the terms:
(30 + 2X)(-20 + 2X) + -1100 = 0

Multiply (30 + 2X) * (-20 + 2X)
(30(-20 + 2X) + 2X * (-20 + 2X)) + -1100 = 0
((-20 * 30 + 2X * 30) + 2X * (-20 + 2X)) + -1100 = 0
((-600 + 60X) + 2X * (-20 + 2X)) + -1100 = 0
(-600 + 60X + (-20 * 2X + 2X * 2X)) + -1100 = 0
(-600 + 60X + (-40X + 4X2)) + -1100 = 0

Combine like terms: 60X + -40X = 20X
(-600 + 20X + 4X2) + -1100 = 0

Reorder the terms:
-600 + -1100 + 20X + 4X2 = 0

Combine like terms: -600 + -1100 = -1700
-1700 + 20X + 4X2 = 0

Solving
-1700 + 20X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-425 + 5X + X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-425 + 5X + X2)' equal to zero and attempt to solve:

Simplifying
-425 + 5X + X2 = 0

Solving
-425 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '425' to each side of the equation.
-425 + 5X + 425 + X2 = 0 + 425

Reorder the terms:
-425 + 425 + 5X + X2 = 0 + 425

Combine like terms: -425 + 425 = 0
0 + 5X + X2 = 0 + 425
5X + X2 = 0 + 425

Combine like terms: 0 + 425 = 425
5X + X2 = 425

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 = 425 + 6.25

Reorder the terms:
6.25 + 5X + X2 = 425 + 6.25

Combine like terms: 425 + 6.25 = 431.25
6.25 + 5X + X2 = 431.25

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = 431.25

Calculate the square root of the right side: 20.766559657

Break this problem into two subproblems by setting 
(X + 2.5) equal to 20.766559657 and -20.766559657.


Subproblem 1
X + 2.5 = 20.766559657

Simplifying
X + 2.5 = 20.766559657

Reorder the terms:
2.5 + X = 20.766559657

Solving
2.5 + X = 20.766559657

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 = 20.766559657 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = 20.766559657 + -2.5
X = 20.766559657 + -2.5

Combine like terms: 20.766559657 + -2.5 = 18.266559657
X = 18.266559657

Simplifying
X = 18.266559657


Subproblem 2
X + 2.5 = -20.766559657

Simplifying
X + 2.5 = -20.766559657

Reorder the terms:
2.5 + X = -20.766559657

Solving
2.5 + X = -20.766559657

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 = -20.766559657 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + X = -20.766559657 + -2.5
X = -20.766559657 + -2.5

Combine like terms: -20.766559657 + -2.5 = -23.266559657
X = -23.266559657

Simplifying
X = -23.266559657


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {18.266559657, -23.266559657}
Solution
X = {18.266559657, -23.266559657}

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