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Simplifying 14r2 + -19r = 6r2 + 15 Reorder the terms: -19r + 14r2 = 6r2 + 15 Reorder the terms: -19r + 14r2 = 15 + 6r2 Solving -19r + 14r2 = 15 + 6r2 Solving for variable 'r'. Reorder the terms: -15 + -19r + 14r2 + -6r2 = 15 + 6r2 + -15 + -6r2 Combine like terms: 14r2 + -6r2 = 8r2 -15 + -19r + 8r2 = 15 + 6r2 + -15 + -6r2 Reorder the terms: -15 + -19r + 8r2 = 15 + -15 + 6r2 + -6r2 Combine like terms: 15 + -15 = 0 -15 + -19r + 8r2 = 0 + 6r2 + -6r2 -15 + -19r + 8r2 = 6r2 + -6r2 Combine like terms: 6r2 + -6r2 = 0 -15 + -19r + 8r2 = 0 Factor a trinomial. (-5 + -8r)(3 + -1r) = 0Subproblem 1
Set the factor '(-5 + -8r)' equal to zero and attempt to solve: Simplifying -5 + -8r = 0 Solving -5 + -8r = 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 + -8r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8r = 0 + 5 -8r = 0 + 5 Combine like terms: 0 + 5 = 5 -8r = 5 Divide each side by '-8'. r = -0.625 Simplifying r = -0.625Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {-0.625, 3}
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