(r-2)(r+14)=11

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Solution for (r-2)(r+14)=11 equation:


Simplifying
(r + -2)(r + 14) = 11

Reorder the terms:
(-2 + r)(r + 14) = 11

Reorder the terms:
(-2 + r)(14 + r) = 11

Multiply (-2 + r) * (14 + r)
(-2(14 + r) + r(14 + r)) = 11
((14 * -2 + r * -2) + r(14 + r)) = 11
((-28 + -2r) + r(14 + r)) = 11
(-28 + -2r + (14 * r + r * r)) = 11
(-28 + -2r + (14r + r2)) = 11

Combine like terms: -2r + 14r = 12r
(-28 + 12r + r2) = 11

Solving
-28 + 12r + r2 = 11

Solving for variable 'r'.

Reorder the terms:
-28 + -11 + 12r + r2 = 11 + -11

Combine like terms: -28 + -11 = -39
-39 + 12r + r2 = 11 + -11

Combine like terms: 11 + -11 = 0
-39 + 12r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + 12r + 39 + r2 = 0 + 39

Reorder the terms:
-39 + 39 + 12r + r2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + 12r + r2 = 0 + 39
12r + r2 = 0 + 39

Combine like terms: 0 + 39 = 39
12r + r2 = 39

The r term is 12r.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12r + 36 + r2 = 39 + 36

Reorder the terms:
36 + 12r + r2 = 39 + 36

Combine like terms: 39 + 36 = 75
36 + 12r + r2 = 75

Factor a perfect square on the left side:
(r + 6)(r + 6) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(r + 6) equal to 8.660254038 and -8.660254038.

Subproblem 1

r + 6 = 8.660254038 Simplifying r + 6 = 8.660254038 Reorder the terms: 6 + r = 8.660254038 Solving 6 + r = 8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + r = 8.660254038 + -6 r = 8.660254038 + -6 Combine like terms: 8.660254038 + -6 = 2.660254038 r = 2.660254038 Simplifying r = 2.660254038

Subproblem 2

r + 6 = -8.660254038 Simplifying r + 6 = -8.660254038 Reorder the terms: 6 + r = -8.660254038 Solving 6 + r = -8.660254038 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -8.660254038 + -6 Combine like terms: 6 + -6 = 0 0 + r = -8.660254038 + -6 r = -8.660254038 + -6 Combine like terms: -8.660254038 + -6 = -14.660254038 r = -14.660254038 Simplifying r = -14.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.660254038, -14.660254038}

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