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Simplifying -1r2 + r = 7r + 9 Reorder the terms: r + -1r2 = 7r + 9 Reorder the terms: r + -1r2 = 9 + 7r Solving r + -1r2 = 9 + 7r Solving for variable 'r'. Reorder the terms: -9 + r + -7r + -1r2 = 9 + 7r + -9 + -7r Combine like terms: r + -7r = -6r -9 + -6r + -1r2 = 9 + 7r + -9 + -7r Reorder the terms: -9 + -6r + -1r2 = 9 + -9 + 7r + -7r Combine like terms: 9 + -9 = 0 -9 + -6r + -1r2 = 0 + 7r + -7r -9 + -6r + -1r2 = 7r + -7r Combine like terms: 7r + -7r = 0 -9 + -6r + -1r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 6r + r2) = 0 Factor a trinomial. -1((3 + r)(3 + r)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve: Simplifying 3 + r = 0 Solving 3 + r = 0 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 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r = 0 + -3 r = 0 + -3 Combine like terms: 0 + -3 = -3 r = -3 Simplifying r = -3Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve: Simplifying 3 + r = 0 Solving 3 + r = 0 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 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r = 0 + -3 r = 0 + -3 Combine like terms: 0 + -3 = -3 r = -3 Simplifying r = -3Solution
r = {-3, -3}
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