2x(x+25)=180

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


Simplifying
2x(x + 25) = 180

Reorder the terms:
2x(25 + x) = 180
(25 * 2x + x * 2x) = 180
(50x + 2x2) = 180

Solving
50x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 50x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 50x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 25x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 25x + x2 = 0

Solving
-90 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 25x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 25x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 25x + x2 = 0 + 90
25x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
25x + x2 = 90

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 90 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 90 + 156.25

Combine like terms: 90 + 156.25 = 246.25
156.25 + 25x + x2 = 246.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 246.25

Calculate the square root of the right side: 15.692354826

Break this problem into two subproblems by setting 
(x + 12.5) equal to 15.692354826 and -15.692354826.


Subproblem 1
x + 12.5 = 15.692354826

Simplifying
x + 12.5 = 15.692354826

Reorder the terms:
12.5 + x = 15.692354826

Solving
12.5 + x = 15.692354826

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 15.692354826 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 15.692354826 + -12.5
x = 15.692354826 + -12.5

Combine like terms: 15.692354826 + -12.5 = 3.192354826
x = 3.192354826

Simplifying
x = 3.192354826


Subproblem 2
x + 12.5 = -15.692354826

Simplifying
x + 12.5 = -15.692354826

Reorder the terms:
12.5 + x = -15.692354826

Solving
12.5 + x = -15.692354826

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -15.692354826 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -15.692354826 + -12.5
x = -15.692354826 + -12.5

Combine like terms: -15.692354826 + -12.5 = -28.192354826
x = -28.192354826

Simplifying
x = -28.192354826


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.192354826, -28.192354826}
Solution
x = {3.192354826, -28.192354826}

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