2x(x+50)=180

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Solution for 2x(x+50)=180 equation: 


Simplifying
2x(x + 50) = 180

Reorder the terms:
2x(50 + x) = 180
(50 * 2x + x * 2x) = 180
(100x + 2x2) = 180

Solving
100x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 100x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 100x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 50x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 50x + x2 = 0

Solving
-90 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 50x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 50x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 50x + x2 = 0 + 90
50x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
50x + x2 = 90

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 90 + 625

Reorder the terms:
625 + 50x + x2 = 90 + 625

Combine like terms: 90 + 625 = 715
625 + 50x + x2 = 715

Factor a perfect square on the left side:
(x + 25)(x + 25) = 715

Calculate the square root of the right side: 26.739483914

Break this problem into two subproblems by setting 
(x + 25) equal to 26.739483914 and -26.739483914.


Subproblem 1
x + 25 = 26.739483914

Simplifying
x + 25 = 26.739483914

Reorder the terms:
25 + x = 26.739483914

Solving
25 + x = 26.739483914

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 26.739483914 + -25

Combine like terms: 25 + -25 = 0
0 + x = 26.739483914 + -25
x = 26.739483914 + -25

Combine like terms: 26.739483914 + -25 = 1.739483914
x = 1.739483914

Simplifying
x = 1.739483914


Subproblem 2
x + 25 = -26.739483914

Simplifying
x + 25 = -26.739483914

Reorder the terms:
25 + x = -26.739483914

Solving
25 + x = -26.739483914

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -26.739483914 + -25

Combine like terms: 25 + -25 = 0
0 + x = -26.739483914 + -25
x = -26.739483914 + -25

Combine like terms: -26.739483914 + -25 = -51.739483914
x = -51.739483914

Simplifying
x = -51.739483914


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.739483914, -51.739483914}
Solution
x = {1.739483914, -51.739483914}

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