(r-2)(r+16)=-6

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Solution for (r-2)(r+16)=-6 equation:


Simplifying
(r + -2)(r + 16) = -6

Reorder the terms:
(-2 + r)(r + 16) = -6

Reorder the terms:
(-2 + r)(16 + r) = -6

Multiply (-2 + r) * (16 + r)
(-2(16 + r) + r(16 + r)) = -6
((16 * -2 + r * -2) + r(16 + r)) = -6
((-32 + -2r) + r(16 + r)) = -6
(-32 + -2r + (16 * r + r * r)) = -6
(-32 + -2r + (16r + r2)) = -6

Combine like terms: -2r + 16r = 14r
(-32 + 14r + r2) = -6

Solving
-32 + 14r + r2 = -6

Solving for variable 'r'.

Reorder the terms:
-32 + 6 + 14r + r2 = -6 + 6

Combine like terms: -32 + 6 = -26
-26 + 14r + r2 = -6 + 6

Combine like terms: -6 + 6 = 0
-26 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 14r + 26 + r2 = 0 + 26

Reorder the terms:
-26 + 26 + 14r + r2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 14r + r2 = 0 + 26
14r + r2 = 0 + 26

Combine like terms: 0 + 26 = 26
14r + r2 = 26

The r term is 14r.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14r + 49 + r2 = 26 + 49

Reorder the terms:
49 + 14r + r2 = 26 + 49

Combine like terms: 26 + 49 = 75
49 + 14r + r2 = 75

Factor a perfect square on the left side:
(r + 7)(r + 7) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(r + 7) equal to 8.660254038 and -8.660254038.

Subproblem 1

r + 7 = 8.660254038 Simplifying r + 7 = 8.660254038 Reorder the terms: 7 + r = 8.660254038 Solving 7 + r = 8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + r = 8.660254038 + -7 r = 8.660254038 + -7 Combine like terms: 8.660254038 + -7 = 1.660254038 r = 1.660254038 Simplifying r = 1.660254038

Subproblem 2

r + 7 = -8.660254038 Simplifying r + 7 = -8.660254038 Reorder the terms: 7 + r = -8.660254038 Solving 7 + r = -8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -8.660254038 + -7 Combine like terms: 7 + -7 = 0 0 + r = -8.660254038 + -7 r = -8.660254038 + -7 Combine like terms: -8.660254038 + -7 = -15.660254038 r = -15.660254038 Simplifying r = -15.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.660254038, -15.660254038}

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