(10+2x)(30+2x)=80

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Solution for (10+2x)(30+2x)=80 equation: 


Simplifying
(10 + 2x)(30 + 2x) = 80

Multiply (10 + 2x) * (30 + 2x)
(10(30 + 2x) + 2x * (30 + 2x)) = 80
((30 * 10 + 2x * 10) + 2x * (30 + 2x)) = 80
((300 + 20x) + 2x * (30 + 2x)) = 80
(300 + 20x + (30 * 2x + 2x * 2x)) = 80
(300 + 20x + (60x + 4x2)) = 80

Combine like terms: 20x + 60x = 80x
(300 + 80x + 4x2) = 80

Solving
300 + 80x + 4x2 = 80

Solving for variable 'x'.

Reorder the terms:
300 + -80 + 80x + 4x2 = 80 + -80

Combine like terms: 300 + -80 = 220
220 + 80x + 4x2 = 80 + -80

Combine like terms: 80 + -80 = 0
220 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(55 + 20x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(55 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
55 + 20x + x2 = 0

Solving
55 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-55' to each side of the equation.
55 + 20x + -55 + x2 = 0 + -55

Reorder the terms:
55 + -55 + 20x + x2 = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 20x + x2 = 0 + -55
20x + x2 = 0 + -55

Combine like terms: 0 + -55 = -55
20x + x2 = -55

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -55 + 100

Reorder the terms:
100 + 20x + x2 = -55 + 100

Combine like terms: -55 + 100 = 45
100 + 20x + x2 = 45

Factor a perfect square on the left side:
(x + 10)(x + 10) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 10) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + 10 = 6.708203933

Simplifying
x + 10 = 6.708203933

Reorder the terms:
10 + x = 6.708203933

Solving
10 + x = 6.708203933

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 6.708203933 + -10

Combine like terms: 10 + -10 = 0
0 + x = 6.708203933 + -10
x = 6.708203933 + -10

Combine like terms: 6.708203933 + -10 = -3.291796067
x = -3.291796067

Simplifying
x = -3.291796067


Subproblem 2
x + 10 = -6.708203933

Simplifying
x + 10 = -6.708203933

Reorder the terms:
10 + x = -6.708203933

Solving
10 + x = -6.708203933

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -6.708203933 + -10

Combine like terms: 10 + -10 = 0
0 + x = -6.708203933 + -10
x = -6.708203933 + -10

Combine like terms: -6.708203933 + -10 = -16.708203933
x = -16.708203933

Simplifying
x = -16.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.291796067, -16.708203933}
Solution
x = {-3.291796067, -16.708203933}

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