5x(2x+40)=360

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Solution for 5x(2x+40)=360 equation: 


Simplifying
5x(2x + 40) = 360

Reorder the terms:
5x(40 + 2x) = 360
(40 * 5x + 2x * 5x) = 360
(200x + 10x2) = 360

Solving
200x + 10x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 200x + 10x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 200x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-36 + 20x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-36 + 20x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 20x + x2 = 0

Solving
-36 + 20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 20x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 20x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 20x + x2 = 0 + 36
20x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
20x + x2 = 36

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 36 + 100

Reorder the terms:
100 + 20x + x2 = 36 + 100

Combine like terms: 36 + 100 = 136
100 + 20x + x2 = 136

Factor a perfect square on the left side:
(x + 10)(x + 10) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + 10) equal to 11.66190379 and -11.66190379.


Subproblem 1
x + 10 = 11.66190379

Simplifying
x + 10 = 11.66190379

Reorder the terms:
10 + x = 11.66190379

Solving
10 + x = 11.66190379

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 11.66190379 + -10

Combine like terms: 10 + -10 = 0
0 + x = 11.66190379 + -10
x = 11.66190379 + -10

Combine like terms: 11.66190379 + -10 = 1.66190379
x = 1.66190379

Simplifying
x = 1.66190379


Subproblem 2
x + 10 = -11.66190379

Simplifying
x + 10 = -11.66190379

Reorder the terms:
10 + x = -11.66190379

Solving
10 + x = -11.66190379

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -11.66190379 + -10

Combine like terms: 10 + -10 = 0
0 + x = -11.66190379 + -10
x = -11.66190379 + -10

Combine like terms: -11.66190379 + -10 = -21.66190379
x = -21.66190379

Simplifying
x = -21.66190379


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.66190379, -21.66190379}
Solution
x = {1.66190379, -21.66190379}

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