5x(18-4x)=-36

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Solution for 5x(18-4x)=-36 equation: 


Simplifying
5x(18 + -4x) = -36
(18 * 5x + -4x * 5x) = -36
(90x + -20x2) = -36

Solving
90x + -20x2 = -36

Solving for variable 'x'.

Reorder the terms:
36 + 90x + -20x2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 90x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 45x + -10x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + 45x + -10x2)' equal to zero and attempt to solve:

Simplifying
18 + 45x + -10x2 = 0

Solving
18 + 45x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-1.8 + -4.5x + x2 = 0.0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -4.5x + 1.8 + x2 = 0.0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -4.5x + x2 = 0.0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -4.5x + x2 = 0.0 + 1.8
-4.5x + x2 = 0.0 + 1.8

Combine like terms: 0.0 + 1.8 = 1.8
-4.5x + x2 = 1.8

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1.8 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1.8 + 5.0625

Combine like terms: 1.8 + 5.0625 = 6.8625
5.0625 + -4.5x + x2 = 6.8625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.8625

Calculate the square root of the right side: 2.619637379

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.619637379 and -2.619637379.


Subproblem 1
x + -2.25 = 2.619637379

Simplifying
x + -2.25 = 2.619637379

Reorder the terms:
-2.25 + x = 2.619637379

Solving
-2.25 + x = 2.619637379

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.619637379 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.619637379 + 2.25
x = 2.619637379 + 2.25

Combine like terms: 2.619637379 + 2.25 = 4.869637379
x = 4.869637379

Simplifying
x = 4.869637379


Subproblem 2
x + -2.25 = -2.619637379

Simplifying
x + -2.25 = -2.619637379

Reorder the terms:
-2.25 + x = -2.619637379

Solving
-2.25 + x = -2.619637379

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.619637379 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.619637379 + 2.25
x = -2.619637379 + 2.25

Combine like terms: -2.619637379 + 2.25 = -0.369637379
x = -0.369637379

Simplifying
x = -0.369637379


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.869637379, -0.369637379}
Solution
x = {4.869637379, -0.369637379}

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