5x(4x+45)=360

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Solution for 5x(4x+45)=360 equation: 


Simplifying
5x(4x + 45) = 360

Reorder the terms:
5x(45 + 4x) = 360
(45 * 5x + 4x * 5x) = 360
(225x + 20x2) = 360

Solving
225x + 20x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 225x + 20x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 225x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-72 + 45x + 4x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-72 + 45x + 4x2)' equal to zero and attempt to solve:

Simplifying
-72 + 45x + 4x2 = 0

Solving
-72 + 45x + 4x2 = 0

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

Divide each side by '4'.
-18 + 11.25x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 11.25x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 11.25x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 11.25x + x2 = 0 + 18
11.25x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
11.25x + x2 = 18

The x term is 11.25x.  Take half its coefficient (5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
11.25x + 31.640625 + x2 = 18 + 31.640625

Reorder the terms:
31.640625 + 11.25x + x2 = 18 + 31.640625

Combine like terms: 18 + 31.640625 = 49.640625
31.640625 + 11.25x + x2 = 49.640625

Factor a perfect square on the left side:
(x + 5.625)(x + 5.625) = 49.640625

Calculate the square root of the right side: 7.045610336

Break this problem into two subproblems by setting 
(x + 5.625) equal to 7.045610336 and -7.045610336.


Subproblem 1
x + 5.625 = 7.045610336

Simplifying
x + 5.625 = 7.045610336

Reorder the terms:
5.625 + x = 7.045610336

Solving
5.625 + x = 7.045610336

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = 7.045610336 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = 7.045610336 + -5.625
x = 7.045610336 + -5.625

Combine like terms: 7.045610336 + -5.625 = 1.420610336
x = 1.420610336

Simplifying
x = 1.420610336


Subproblem 2
x + 5.625 = -7.045610336

Simplifying
x + 5.625 = -7.045610336

Reorder the terms:
5.625 + x = -7.045610336

Solving
5.625 + x = -7.045610336

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = -7.045610336 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = -7.045610336 + -5.625
x = -7.045610336 + -5.625

Combine like terms: -7.045610336 + -5.625 = -12.670610336
x = -12.670610336

Simplifying
x = -12.670610336


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.420610336, -12.670610336}
Solution
x = {1.420610336, -12.670610336}

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