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Simplifying 8r2 + 10rs + 12rs + 15rs2 = 0 Reorder the terms: 10rs + 12rs + 15rs2 + 8r2 = 0 Combine like terms: 10rs + 12rs = 22rs 22rs + 15rs2 + 8r2 = 0 Solving 22rs + 15rs2 + 8r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(22s + 15s2 + 8r) = 0Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(22s + 15s2 + 8r)' equal to zero and attempt to solve: Simplifying 22s + 15s2 + 8r = 0 Reorder the terms: 8r + 22s + 15s2 = 0 Solving 8r + 22s + 15s2 = 0 Move all terms containing r to the left, all other terms to the right. Add '-22s' to each side of the equation. 8r + 22s + -22s + 15s2 = 0 + -22s Combine like terms: 22s + -22s = 0 8r + 0 + 15s2 = 0 + -22s 8r + 15s2 = 0 + -22s Remove the zero: 8r + 15s2 = -22s Add '-15s2' to each side of the equation. 8r + 15s2 + -15s2 = -22s + -15s2 Combine like terms: 15s2 + -15s2 = 0 8r + 0 = -22s + -15s2 8r = -22s + -15s2 Divide each side by '8'. r = -2.75s + -1.875s2 Simplifying r = -2.75s + -1.875s2Solution
r = {0, -2.75s + -1.875s2}
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