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Simplifying (9 + -8r)(10 + -4r) = 0 Multiply (9 + -8r) * (10 + -4r) (9(10 + -4r) + -8r * (10 + -4r)) = 0 ((10 * 9 + -4r * 9) + -8r * (10 + -4r)) = 0 ((90 + -36r) + -8r * (10 + -4r)) = 0 (90 + -36r + (10 * -8r + -4r * -8r)) = 0 (90 + -36r + (-80r + 32r2)) = 0 Combine like terms: -36r + -80r = -116r (90 + -116r + 32r2) = 0 Solving 90 + -116r + 32r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + -58r + 16r2) = 0 Factor a trinomial. 2((9 + -8r)(5 + -2r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -8r)' equal to zero and attempt to solve: Simplifying 9 + -8r = 0 Solving 9 + -8r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8r = 0 + -9 -8r = 0 + -9 Combine like terms: 0 + -9 = -9 -8r = -9 Divide each side by '-8'. r = 1.125 Simplifying r = 1.125Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 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 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Solution
r = {1.125, 2.5}
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