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Simplifying 32r2 + 16rs + 2s2 = 0 Reorder the terms: 16rs + 32r2 + 2s2 = 0 Solving 16rs + 32r2 + 2s2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(8rs + 16r2 + s2) = 0 Factor a trinomial. 2((4r + s)(4r + s)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4r + s)' equal to zero and attempt to solve: Simplifying 4r + s = 0 Solving 4r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 4r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 4r + 0 = 0 + -1s 4r = 0 + -1s Remove the zero: 4r = -1s Divide each side by '4'. r = -0.25s Simplifying r = -0.25sSubproblem 2
Set the factor '(4r + s)' equal to zero and attempt to solve: Simplifying 4r + s = 0 Solving 4r + s = 0 Move all terms containing r to the left, all other terms to the right. Add '-1s' to each side of the equation. 4r + s + -1s = 0 + -1s Combine like terms: s + -1s = 0 4r + 0 = 0 + -1s 4r = 0 + -1s Remove the zero: 4r = -1s Divide each side by '4'. r = -0.25s Simplifying r = -0.25sSolution
r = {-0.25s, -0.25s}
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