x^2+10x(5x+36)=360

Solution for x^2+10x(5x+36)=360 equation:

Simplifying
x2 + 10x(5x + 36) = 360

Reorder the terms:
x2 + 10x(36 + 5x) = 360
x2 + (36 * 10x + 5x * 10x) = 360
x2 + (360x + 50x2) = 360

Reorder the terms:
360x + x2 + 50x2 = 360

Combine like terms: x2 + 50x2 = 51x2
360x + 51x2 = 360

Solving
360x + 51x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 360x + 51x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 360x + 51x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-120 + 120x + 17x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-120 + 120x + 17x2)' equal to zero and attempt to solve:

Simplifying
-120 + 120x + 17x2 = 0

Solving
-120 + 120x + 17x2 = 0

Begin completing the square.  Divide all terms by
17 the coefficient of the squared term: 

Divide each side by '17'.
-7.058823529 + 7.058823529x + x2 = 0

Move the constant term to the right:

Add '7.058823529' to each side of the equation.
-7.058823529 + 7.058823529x + 7.058823529 + x2 = 0 + 7.058823529

Reorder the terms:
-7.058823529 + 7.058823529 + 7.058823529x + x2 = 0 + 7.058823529

Combine like terms: -7.058823529 + 7.058823529 = 0.000000000
0.000000000 + 7.058823529x + x2 = 0 + 7.058823529
7.058823529x + x2 = 0 + 7.058823529

Combine like terms: 0 + 7.058823529 = 7.058823529
7.058823529x + x2 = 7.058823529

The x term is 7.058823529x.  Take half its coefficient (3.529411765).
Square it (12.45674741) and add it to both sides.

Add '12.45674741' to each side of the equation.
7.058823529x + 12.45674741 + x2 = 7.058823529 + 12.45674741

Reorder the terms:
12.45674741 + 7.058823529x + x2 = 7.058823529 + 12.45674741

Combine like terms: 7.058823529 + 12.45674741 = 19.515570939
12.45674741 + 7.058823529x + x2 = 19.515570939

Factor a perfect square on the left side:
(x + 3.529411765)(x + 3.529411765) = 19.515570939

Calculate the square root of the right side: 4.417643143

Break this problem into two subproblems by setting 
(x + 3.529411765) equal to 4.417643143 and -4.417643143.

Subproblem 1
x + 3.529411765 = 4.417643143

Simplifying
x + 3.529411765 = 4.417643143

Reorder the terms:
3.529411765 + x = 4.417643143

Solving
3.529411765 + x = 4.417643143

Solving for variable 'x'.

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

Add '-3.529411765' to each side of the equation.
3.529411765 + -3.529411765 + x = 4.417643143 + -3.529411765

Combine like terms: 3.529411765 + -3.529411765 = 0.000000000
0.000000000 + x = 4.417643143 + -3.529411765
x = 4.417643143 + -3.529411765

Combine like terms: 4.417643143 + -3.529411765 = 0.888231378
x = 0.888231378

Simplifying
x = 0.888231378

Subproblem 2
x + 3.529411765 = -4.417643143

Simplifying
x + 3.529411765 = -4.417643143

Reorder the terms:
3.529411765 + x = -4.417643143

Solving
3.529411765 + x = -4.417643143

Solving for variable 'x'.

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

Add '-3.529411765' to each side of the equation.
3.529411765 + -3.529411765 + x = -4.417643143 + -3.529411765

Combine like terms: 3.529411765 + -3.529411765 = 0.000000000
0.000000000 + x = -4.417643143 + -3.529411765
x = -4.417643143 + -3.529411765

Combine like terms: -4.417643143 + -3.529411765 = -7.947054908
x = -7.947054908

Simplifying
x = -7.947054908

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.888231378, -7.947054908}
Solution
x = {0.888231378, -7.947054908}