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Simplifying (r + 8)(8r + 1) = 0 Reorder the terms: (8 + r)(8r + 1) = 0 Reorder the terms: (8 + r)(1 + 8r) = 0 Multiply (8 + r) * (1 + 8r) (8(1 + 8r) + r(1 + 8r)) = 0 ((1 * 8 + 8r * 8) + r(1 + 8r)) = 0 ((8 + 64r) + r(1 + 8r)) = 0 (8 + 64r + (1 * r + 8r * r)) = 0 (8 + 64r + (1r + 8r2)) = 0 Combine like terms: 64r + 1r = 65r (8 + 65r + 8r2) = 0 Solving 8 + 65r + 8r2 = 0 Solving for variable 'r'. Factor a trinomial. (8 + r)(1 + 8r) = 0Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Subproblem 2
Set the factor '(1 + 8r)' equal to zero and attempt to solve: Simplifying 1 + 8r = 0 Solving 1 + 8r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 8r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8r = 0 + -1 8r = 0 + -1 Combine like terms: 0 + -1 = -1 8r = -1 Divide each side by '8'. r = -0.125 Simplifying r = -0.125Solution
r = {-8, -0.125}
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