(2x+20)(2x+24)=600

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Solution for (2x+20)(2x+24)=600 equation: 


Simplifying
(2x + 20)(2x + 24) = 600

Reorder the terms:
(20 + 2x)(2x + 24) = 600

Reorder the terms:
(20 + 2x)(24 + 2x) = 600

Multiply (20 + 2x) * (24 + 2x)
(20(24 + 2x) + 2x * (24 + 2x)) = 600
((24 * 20 + 2x * 20) + 2x * (24 + 2x)) = 600
((480 + 40x) + 2x * (24 + 2x)) = 600
(480 + 40x + (24 * 2x + 2x * 2x)) = 600
(480 + 40x + (48x + 4x2)) = 600

Combine like terms: 40x + 48x = 88x
(480 + 88x + 4x2) = 600

Solving
480 + 88x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
480 + -600 + 88x + 4x2 = 600 + -600

Combine like terms: 480 + -600 = -120
-120 + 88x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-120 + 88x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 22x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-30 + 22x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 22x + x2 = 0

Solving
-30 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 22x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 22x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 22x + x2 = 0 + 30
22x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
22x + x2 = 30

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 30 + 121

Reorder the terms:
121 + 22x + x2 = 30 + 121

Combine like terms: 30 + 121 = 151
121 + 22x + x2 = 151

Factor a perfect square on the left side:
(x + 11)(x + 11) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(x + 11) equal to 12.288205727 and -12.288205727.


Subproblem 1
x + 11 = 12.288205727

Simplifying
x + 11 = 12.288205727

Reorder the terms:
11 + x = 12.288205727

Solving
11 + x = 12.288205727

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 12.288205727 + -11

Combine like terms: 11 + -11 = 0
0 + x = 12.288205727 + -11
x = 12.288205727 + -11

Combine like terms: 12.288205727 + -11 = 1.288205727
x = 1.288205727

Simplifying
x = 1.288205727


Subproblem 2
x + 11 = -12.288205727

Simplifying
x + 11 = -12.288205727

Reorder the terms:
11 + x = -12.288205727

Solving
11 + x = -12.288205727

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -12.288205727 + -11

Combine like terms: 11 + -11 = 0
0 + x = -12.288205727 + -11
x = -12.288205727 + -11

Combine like terms: -12.288205727 + -11 = -23.288205727
x = -23.288205727

Simplifying
x = -23.288205727


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.288205727, -23.288205727}
Solution
x = {1.288205727, -23.288205727}

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