(r-2)(r+16)=44

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Solution for (r-2)(r+16)=44 equation:


Simplifying
(r + -2)(r + 16) = 44

Reorder the terms:
(-2 + r)(r + 16) = 44

Reorder the terms:
(-2 + r)(16 + r) = 44

Multiply (-2 + r) * (16 + r)
(-2(16 + r) + r(16 + r)) = 44
((16 * -2 + r * -2) + r(16 + r)) = 44
((-32 + -2r) + r(16 + r)) = 44
(-32 + -2r + (16 * r + r * r)) = 44
(-32 + -2r + (16r + r2)) = 44

Combine like terms: -2r + 16r = 14r
(-32 + 14r + r2) = 44

Solving
-32 + 14r + r2 = 44

Solving for variable 'r'.

Reorder the terms:
-32 + -44 + 14r + r2 = 44 + -44

Combine like terms: -32 + -44 = -76
-76 + 14r + r2 = 44 + -44

Combine like terms: 44 + -44 = 0
-76 + 14r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + 14r + 76 + r2 = 0 + 76

Reorder the terms:
-76 + 76 + 14r + r2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + 14r + r2 = 0 + 76
14r + r2 = 0 + 76

Combine like terms: 0 + 76 = 76
14r + r2 = 76

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 = 76 + 49

Reorder the terms:
49 + 14r + r2 = 76 + 49

Combine like terms: 76 + 49 = 125
49 + 14r + r2 = 125

Factor a perfect square on the left side:
(r + 7)(r + 7) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 7) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 7 = 11.180339887 Simplifying r + 7 = 11.180339887 Reorder the terms: 7 + r = 11.180339887 Solving 7 + r = 11.180339887 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 = 11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = 11.180339887 + -7 r = 11.180339887 + -7 Combine like terms: 11.180339887 + -7 = 4.180339887 r = 4.180339887 Simplifying r = 4.180339887

Subproblem 2

r + 7 = -11.180339887 Simplifying r + 7 = -11.180339887 Reorder the terms: 7 + r = -11.180339887 Solving 7 + r = -11.180339887 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 = -11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = -11.180339887 + -7 r = -11.180339887 + -7 Combine like terms: -11.180339887 + -7 = -18.180339887 r = -18.180339887 Simplifying r = -18.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.180339887, -18.180339887}

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