(2x+20)(x+25)=180

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Solution for (2x+20)(x+25)=180 equation: 


Simplifying
(2x + 20)(x + 25) = 180

Reorder the terms:
(20 + 2x)(x + 25) = 180

Reorder the terms:
(20 + 2x)(25 + x) = 180

Multiply (20 + 2x) * (25 + x)
(20(25 + x) + 2x * (25 + x)) = 180
((25 * 20 + x * 20) + 2x * (25 + x)) = 180
((500 + 20x) + 2x * (25 + x)) = 180
(500 + 20x + (25 * 2x + x * 2x)) = 180
(500 + 20x + (50x + 2x2)) = 180

Combine like terms: 20x + 50x = 70x
(500 + 70x + 2x2) = 180

Solving
500 + 70x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
500 + -180 + 70x + 2x2 = 180 + -180

Combine like terms: 500 + -180 = 320
320 + 70x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
320 + 70x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(160 + 35x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(160 + 35x + x2)' equal to zero and attempt to solve:

Simplifying
160 + 35x + x2 = 0

Solving
160 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-160' to each side of the equation.
160 + 35x + -160 + x2 = 0 + -160

Reorder the terms:
160 + -160 + 35x + x2 = 0 + -160

Combine like terms: 160 + -160 = 0
0 + 35x + x2 = 0 + -160
35x + x2 = 0 + -160

Combine like terms: 0 + -160 = -160
35x + x2 = -160

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -160 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -160 + 306.25

Combine like terms: -160 + 306.25 = 146.25
306.25 + 35x + x2 = 146.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 17.5) equal to 12.093386622 and -12.093386622.


Subproblem 1
x + 17.5 = 12.093386622

Simplifying
x + 17.5 = 12.093386622

Reorder the terms:
17.5 + x = 12.093386622

Solving
17.5 + x = 12.093386622

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 12.093386622 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 12.093386622 + -17.5
x = 12.093386622 + -17.5

Combine like terms: 12.093386622 + -17.5 = -5.406613378
x = -5.406613378

Simplifying
x = -5.406613378


Subproblem 2
x + 17.5 = -12.093386622

Simplifying
x + 17.5 = -12.093386622

Reorder the terms:
17.5 + x = -12.093386622

Solving
17.5 + x = -12.093386622

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -12.093386622 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -12.093386622 + -17.5
x = -12.093386622 + -17.5

Combine like terms: -12.093386622 + -17.5 = -29.593386622
x = -29.593386622

Simplifying
x = -29.593386622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.406613378, -29.593386622}
Solution
x = {-5.406613378, -29.593386622}

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