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Simplifying (r + -1)(r + -1) = 36 Reorder the terms: (-1 + r)(r + -1) = 36 Reorder the terms: (-1 + r)(-1 + r) = 36 Multiply (-1 + r) * (-1 + r) (-1(-1 + r) + r(-1 + r)) = 36 ((-1 * -1 + r * -1) + r(-1 + r)) = 36 ((1 + -1r) + r(-1 + r)) = 36 (1 + -1r + (-1 * r + r * r)) = 36 (1 + -1r + (-1r + r2)) = 36 Combine like terms: -1r + -1r = -2r (1 + -2r + r2) = 36 Solving 1 + -2r + r2 = 36 Solving for variable 'r'. Reorder the terms: 1 + -36 + -2r + r2 = 36 + -36 Combine like terms: 1 + -36 = -35 -35 + -2r + r2 = 36 + -36 Combine like terms: 36 + -36 = 0 -35 + -2r + r2 = 0 Factor a trinomial. (-5 + -1r)(7 + -1r) = 0Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Solution
r = {-5, 7}
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