(r-4)(r+8)=-16

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Solution for (r-4)(r+8)=-16 equation: 


Simplifying
(r + -4)(r + 8) = -16

Reorder the terms:
(-4 + r)(r + 8) = -16

Reorder the terms:
(-4 + r)(8 + r) = -16

Multiply (-4 + r) * (8 + r)
(-4(8 + r) + r(8 + r)) = -16
((8 * -4 + r * -4) + r(8 + r)) = -16
((-32 + -4r) + r(8 + r)) = -16
(-32 + -4r + (8 * r + r * r)) = -16
(-32 + -4r + (8r + r2)) = -16

Combine like terms: -4r + 8r = 4r
(-32 + 4r + r2) = -16

Solving
-32 + 4r + r2 = -16

Solving for variable 'r'.

Reorder the terms:
-32 + 16 + 4r + r2 = -16 + 16

Combine like terms: -32 + 16 = -16
-16 + 4r + r2 = -16 + 16

Combine like terms: -16 + 16 = 0
-16 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + 4r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4r + r2 = 0 + 16
4r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
4r + r2 = 16

The r term is 4r.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4r + 4 + r2 = 16 + 4

Reorder the terms:
4 + 4r + r2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4r + r2 = 20

Factor a perfect square on the left side:
(r + 2)(r + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(r + 2) equal to 4.472135955 and -4.472135955.


Subproblem 1
r + 2 = 4.472135955

Simplifying
r + 2 = 4.472135955

Reorder the terms:
2 + r = 4.472135955

Solving
2 + r = 4.472135955

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = 4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + r = 4.472135955 + -2
r = 4.472135955 + -2

Combine like terms: 4.472135955 + -2 = 2.472135955
r = 2.472135955

Simplifying
r = 2.472135955


Subproblem 2
r + 2 = -4.472135955

Simplifying
r + 2 = -4.472135955

Reorder the terms:
2 + r = -4.472135955

Solving
2 + r = -4.472135955

Solving for variable 'r'.

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

Add '-2' to each side of the equation.
2 + -2 + r = -4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + r = -4.472135955 + -2
r = -4.472135955 + -2

Combine like terms: -4.472135955 + -2 = -6.472135955
r = -6.472135955

Simplifying
r = -6.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.472135955, -6.472135955}

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