2x(x+75)=180

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Solution for 2x(x+75)=180 equation: 


Simplifying
2x(x + 75) = 180

Reorder the terms:
2x(75 + x) = 180
(75 * 2x + x * 2x) = 180
(150x + 2x2) = 180

Solving
150x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 150x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 150x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 75x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 75x + x2)' equal to zero and attempt to solve:

Simplifying
-90 + 75x + x2 = 0

Solving
-90 + 75x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 75x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 75x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 75x + x2 = 0 + 90
75x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
75x + x2 = 90

The x term is 75x.  Take half its coefficient (37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
75x + 1406.25 + x2 = 90 + 1406.25

Reorder the terms:
1406.25 + 75x + x2 = 90 + 1406.25

Combine like terms: 90 + 1406.25 = 1496.25
1406.25 + 75x + x2 = 1496.25

Factor a perfect square on the left side:
(x + 37.5)(x + 37.5) = 1496.25

Calculate the square root of the right side: 38.681390875

Break this problem into two subproblems by setting 
(x + 37.5) equal to 38.681390875 and -38.681390875.


Subproblem 1
x + 37.5 = 38.681390875

Simplifying
x + 37.5 = 38.681390875

Reorder the terms:
37.5 + x = 38.681390875

Solving
37.5 + x = 38.681390875

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = 38.681390875 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = 38.681390875 + -37.5
x = 38.681390875 + -37.5

Combine like terms: 38.681390875 + -37.5 = 1.181390875
x = 1.181390875

Simplifying
x = 1.181390875


Subproblem 2
x + 37.5 = -38.681390875

Simplifying
x + 37.5 = -38.681390875

Reorder the terms:
37.5 + x = -38.681390875

Solving
37.5 + x = -38.681390875

Solving for variable 'x'.

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

Add '-37.5' to each side of the equation.
37.5 + -37.5 + x = -38.681390875 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + x = -38.681390875 + -37.5
x = -38.681390875 + -37.5

Combine like terms: -38.681390875 + -37.5 = -76.181390875
x = -76.181390875

Simplifying
x = -76.181390875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.181390875, -76.181390875}
Solution
x = {1.181390875, -76.181390875}

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