(r-2)(r+8)=100

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Solution for (r-2)(r+8)=100 equation:


Simplifying
(r + -2)(r + 8) = 100

Reorder the terms:
(-2 + r)(r + 8) = 100

Reorder the terms:
(-2 + r)(8 + r) = 100

Multiply (-2 + r) * (8 + r)
(-2(8 + r) + r(8 + r)) = 100
((8 * -2 + r * -2) + r(8 + r)) = 100
((-16 + -2r) + r(8 + r)) = 100
(-16 + -2r + (8 * r + r * r)) = 100
(-16 + -2r + (8r + r2)) = 100

Combine like terms: -2r + 8r = 6r
(-16 + 6r + r2) = 100

Solving
-16 + 6r + r2 = 100

Solving for variable 'r'.

Reorder the terms:
-16 + -100 + 6r + r2 = 100 + -100

Combine like terms: -16 + -100 = -116
-116 + 6r + r2 = 100 + -100

Combine like terms: 100 + -100 = 0
-116 + 6r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '116' to each side of the equation.
-116 + 6r + 116 + r2 = 0 + 116

Reorder the terms:
-116 + 116 + 6r + r2 = 0 + 116

Combine like terms: -116 + 116 = 0
0 + 6r + r2 = 0 + 116
6r + r2 = 0 + 116

Combine like terms: 0 + 116 = 116
6r + r2 = 116

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = 116 + 9

Reorder the terms:
9 + 6r + r2 = 116 + 9

Combine like terms: 116 + 9 = 125
9 + 6r + r2 = 125

Factor a perfect square on the left side:
(r + 3)(r + 3) = 125

Calculate the square root of the right side: 11.180339887

Break this problem into two subproblems by setting 
(r + 3) equal to 11.180339887 and -11.180339887.

Subproblem 1

r + 3 = 11.180339887 Simplifying r + 3 = 11.180339887 Reorder the terms: 3 + r = 11.180339887 Solving 3 + r = 11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + r = 11.180339887 + -3 r = 11.180339887 + -3 Combine like terms: 11.180339887 + -3 = 8.180339887 r = 8.180339887 Simplifying r = 8.180339887

Subproblem 2

r + 3 = -11.180339887 Simplifying r + 3 = -11.180339887 Reorder the terms: 3 + r = -11.180339887 Solving 3 + r = -11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + r = -11.180339887 + -3 r = -11.180339887 + -3 Combine like terms: -11.180339887 + -3 = -14.180339887 r = -14.180339887 Simplifying r = -14.180339887

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.180339887, -14.180339887}

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