4x(x+2)+9(3x+4)=18

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Solution for 4x(x+2)+9(3x+4)=18 equation: 


Simplifying
4x(x + 2) + 9(3x + 4) = 18

Reorder the terms:
4x(2 + x) + 9(3x + 4) = 18
(2 * 4x + x * 4x) + 9(3x + 4) = 18
(8x + 4x2) + 9(3x + 4) = 18

Reorder the terms:
8x + 4x2 + 9(4 + 3x) = 18
8x + 4x2 + (4 * 9 + 3x * 9) = 18
8x + 4x2 + (36 + 27x) = 18

Reorder the terms:
36 + 8x + 27x + 4x2 = 18

Combine like terms: 8x + 27x = 35x
36 + 35x + 4x2 = 18

Solving
36 + 35x + 4x2 = 18

Solving for variable 'x'.

Reorder the terms:
36 + -18 + 35x + 4x2 = 18 + -18

Combine like terms: 36 + -18 = 18
18 + 35x + 4x2 = 18 + -18

Combine like terms: 18 + -18 = 0
18 + 35x + 4x2 = 0

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

Divide each side by '4'.
4.5 + 8.75x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 8.75x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 8.75x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 8.75x + x2 = 0 + -4.5
8.75x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
8.75x + x2 = -4.5

The x term is 8.75x.  Take half its coefficient (4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
8.75x + 19.140625 + x2 = -4.5 + 19.140625

Reorder the terms:
19.140625 + 8.75x + x2 = -4.5 + 19.140625

Combine like terms: -4.5 + 19.140625 = 14.640625
19.140625 + 8.75x + x2 = 14.640625

Factor a perfect square on the left side:
(x + 4.375)(x + 4.375) = 14.640625

Calculate the square root of the right side: 3.826306966

Break this problem into two subproblems by setting 
(x + 4.375) equal to 3.826306966 and -3.826306966.


Subproblem 1
x + 4.375 = 3.826306966

Simplifying
x + 4.375 = 3.826306966

Reorder the terms:
4.375 + x = 3.826306966

Solving
4.375 + x = 3.826306966

Solving for variable 'x'.

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

Add '-4.375' to each side of the equation.
4.375 + -4.375 + x = 3.826306966 + -4.375

Combine like terms: 4.375 + -4.375 = 0.000
0.000 + x = 3.826306966 + -4.375
x = 3.826306966 + -4.375

Combine like terms: 3.826306966 + -4.375 = -0.548693034
x = -0.548693034

Simplifying
x = -0.548693034


Subproblem 2
x + 4.375 = -3.826306966

Simplifying
x + 4.375 = -3.826306966

Reorder the terms:
4.375 + x = -3.826306966

Solving
4.375 + x = -3.826306966

Solving for variable 'x'.

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

Add '-4.375' to each side of the equation.
4.375 + -4.375 + x = -3.826306966 + -4.375

Combine like terms: 4.375 + -4.375 = 0.000
0.000 + x = -3.826306966 + -4.375
x = -3.826306966 + -4.375

Combine like terms: -3.826306966 + -4.375 = -8.201306966
x = -8.201306966

Simplifying
x = -8.201306966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.548693034, -8.201306966}

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