-4x(x+9)=-16

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Solution for -4x(x+9)=-16 equation: 


Simplifying
-4x(x + 9) = -16

Reorder the terms:
-4x(9 + x) = -16
(9 * -4x + x * -4x) = -16
(-36x + -4x2) = -16

Solving
-36x + -4x2 = -16

Solving for variable 'x'.

Reorder the terms:
16 + -36x + -4x2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -36x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -9x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(4 + -9x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + -9x + -1x2 = 0

Solving
4 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 9x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 9x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 9x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 9x + x2 = 0 + 4
9x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
9x + x2 = 4

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 = 4 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 4 + 20.25

Combine like terms: 4 + 20.25 = 24.25
20.25 + 9x + x2 = 24.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + 4.5 = 4.924428901

Simplifying
x + 4.5 = 4.924428901

Reorder the terms:
4.5 + x = 4.924428901

Solving
4.5 + x = 4.924428901

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 = 4.924428901 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.924428901 + -4.5
x = 4.924428901 + -4.5

Combine like terms: 4.924428901 + -4.5 = 0.424428901
x = 0.424428901

Simplifying
x = 0.424428901


Subproblem 2
x + 4.5 = -4.924428901

Simplifying
x + 4.5 = -4.924428901

Reorder the terms:
4.5 + x = -4.924428901

Solving
4.5 + x = -4.924428901

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 = -4.924428901 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.924428901 + -4.5
x = -4.924428901 + -4.5

Combine like terms: -4.924428901 + -4.5 = -9.424428901
x = -9.424428901

Simplifying
x = -9.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.424428901, -9.424428901}
Solution
x = {0.424428901, -9.424428901}

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