(5x+17)(4x+28)=180

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Solution for (5x+17)(4x+28)=180 equation: 


Simplifying
(5x + 17)(4x + 28) = 180

Reorder the terms:
(17 + 5x)(4x + 28) = 180

Reorder the terms:
(17 + 5x)(28 + 4x) = 180

Multiply (17 + 5x) * (28 + 4x)
(17(28 + 4x) + 5x * (28 + 4x)) = 180
((28 * 17 + 4x * 17) + 5x * (28 + 4x)) = 180
((476 + 68x) + 5x * (28 + 4x)) = 180
(476 + 68x + (28 * 5x + 4x * 5x)) = 180
(476 + 68x + (140x + 20x2)) = 180

Combine like terms: 68x + 140x = 208x
(476 + 208x + 20x2) = 180

Solving
476 + 208x + 20x2 = 180

Solving for variable 'x'.

Reorder the terms:
476 + -180 + 208x + 20x2 = 180 + -180

Combine like terms: 476 + -180 = 296
296 + 208x + 20x2 = 180 + -180

Combine like terms: 180 + -180 = 0
296 + 208x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(74 + 52x + 5x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(74 + 52x + 5x2)' equal to zero and attempt to solve:

Simplifying
74 + 52x + 5x2 = 0

Solving
74 + 52x + 5x2 = 0

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

Divide each side by '5'.
14.8 + 10.4x + x2 = 0

Move the constant term to the right:

Add '-14.8' to each side of the equation.
14.8 + 10.4x + -14.8 + x2 = 0 + -14.8

Reorder the terms:
14.8 + -14.8 + 10.4x + x2 = 0 + -14.8

Combine like terms: 14.8 + -14.8 = 0.0
0.0 + 10.4x + x2 = 0 + -14.8
10.4x + x2 = 0 + -14.8

Combine like terms: 0 + -14.8 = -14.8
10.4x + x2 = -14.8

The x term is 10.4x.  Take half its coefficient (5.2).
Square it (27.04) and add it to both sides.

Add '27.04' to each side of the equation.
10.4x + 27.04 + x2 = -14.8 + 27.04

Reorder the terms:
27.04 + 10.4x + x2 = -14.8 + 27.04

Combine like terms: -14.8 + 27.04 = 12.24
27.04 + 10.4x + x2 = 12.24

Factor a perfect square on the left side:
(x + 5.2)(x + 5.2) = 12.24

Calculate the square root of the right side: 3.498571137

Break this problem into two subproblems by setting 
(x + 5.2) equal to 3.498571137 and -3.498571137.


Subproblem 1
x + 5.2 = 3.498571137

Simplifying
x + 5.2 = 3.498571137

Reorder the terms:
5.2 + x = 3.498571137

Solving
5.2 + x = 3.498571137

Solving for variable 'x'.

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

Add '-5.2' to each side of the equation.
5.2 + -5.2 + x = 3.498571137 + -5.2

Combine like terms: 5.2 + -5.2 = 0.0
0.0 + x = 3.498571137 + -5.2
x = 3.498571137 + -5.2

Combine like terms: 3.498571137 + -5.2 = -1.701428863
x = -1.701428863

Simplifying
x = -1.701428863


Subproblem 2
x + 5.2 = -3.498571137

Simplifying
x + 5.2 = -3.498571137

Reorder the terms:
5.2 + x = -3.498571137

Solving
5.2 + x = -3.498571137

Solving for variable 'x'.

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

Add '-5.2' to each side of the equation.
5.2 + -5.2 + x = -3.498571137 + -5.2

Combine like terms: 5.2 + -5.2 = 0.0
0.0 + x = -3.498571137 + -5.2
x = -3.498571137 + -5.2

Combine like terms: -3.498571137 + -5.2 = -8.698571137
x = -8.698571137

Simplifying
x = -8.698571137


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.701428863, -8.698571137}
Solution
x = {-1.701428863, -8.698571137}

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