3x(x+9)=-48

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Solution for 3x(x+9)=-48 equation: 


Simplifying
3x(x + 9) = -48

Reorder the terms:
3x(9 + x) = -48
(9 * 3x + x * 3x) = -48
(27x + 3x2) = -48

Solving
27x + 3x2 = -48

Solving for variable 'x'.

Reorder the terms:
48 + 27x + 3x2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 9x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(16 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 9x + x2 = 0

Solving
16 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 9x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 9x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 9x + x2 = 0 + -16
9x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
9x + x2 = -16

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -16 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -16 + 20.25

Combine like terms: -16 + 20.25 = 4.25
20.25 + 9x + x2 = 4.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 4.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + 4.5 = 2.061552813

Simplifying
x + 4.5 = 2.061552813

Reorder the terms:
4.5 + x = 2.061552813

Solving
4.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 2.061552813 + -4.5
x = 2.061552813 + -4.5

Combine like terms: 2.061552813 + -4.5 = -2.438447187
x = -2.438447187

Simplifying
x = -2.438447187


Subproblem 2
x + 4.5 = -2.061552813

Simplifying
x + 4.5 = -2.061552813

Reorder the terms:
4.5 + x = -2.061552813

Solving
4.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -2.061552813 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -2.061552813 + -4.5
x = -2.061552813 + -4.5

Combine like terms: -2.061552813 + -4.5 = -6.561552813
x = -6.561552813

Simplifying
x = -6.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.438447187, -6.561552813}
Solution
x = {-2.438447187, -6.561552813}

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