(2x+8)(2x+10)=152

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Solution for (2x+8)(2x+10)=152 equation: 


Simplifying
(2x + 8)(2x + 10) = 152

Reorder the terms:
(8 + 2x)(2x + 10) = 152

Reorder the terms:
(8 + 2x)(10 + 2x) = 152

Multiply (8 + 2x) * (10 + 2x)
(8(10 + 2x) + 2x * (10 + 2x)) = 152
((10 * 8 + 2x * 8) + 2x * (10 + 2x)) = 152
((80 + 16x) + 2x * (10 + 2x)) = 152
(80 + 16x + (10 * 2x + 2x * 2x)) = 152
(80 + 16x + (20x + 4x2)) = 152

Combine like terms: 16x + 20x = 36x
(80 + 36x + 4x2) = 152

Solving
80 + 36x + 4x2 = 152

Solving for variable 'x'.

Reorder the terms:
80 + -152 + 36x + 4x2 = 152 + -152

Combine like terms: 80 + -152 = -72
-72 + 36x + 4x2 = 152 + -152

Combine like terms: 152 + -152 = 0
-72 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-18 + 9x + x2 = 0

Solving
-18 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 9x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9x + x2 = 0 + 18
9x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
9x + x2 = 18

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 18 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + 9x + x2 = 38.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + 4.5 = 6.184658438

Simplifying
x + 4.5 = 6.184658438

Reorder the terms:
4.5 + x = 6.184658438

Solving
4.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.184658438 + -4.5
x = 6.184658438 + -4.5

Combine like terms: 6.184658438 + -4.5 = 1.684658438
x = 1.684658438

Simplifying
x = 1.684658438


Subproblem 2
x + 4.5 = -6.184658438

Simplifying
x + 4.5 = -6.184658438

Reorder the terms:
4.5 + x = -6.184658438

Solving
4.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.184658438 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.184658438 + -4.5
x = -6.184658438 + -4.5

Combine like terms: -6.184658438 + -4.5 = -10.684658438
x = -10.684658438

Simplifying
x = -10.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.684658438, -10.684658438}
Solution
x = {1.684658438, -10.684658438}

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