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Simplifying 100m2 + 410mp + -180p2 = 0 Reorder the terms: 410mp + 100m2 + -180p2 = 0 Solving 410mp + 100m2 + -180p2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '10'. 10(41mp + 10m2 + -18p2) = 0 Factor a trinomial. 10((5m + -2p)(2m + 9p)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5m + -2p)' equal to zero and attempt to solve: Simplifying 5m + -2p = 0 Solving 5m + -2p = 0 Move all terms containing m to the left, all other terms to the right. Add '2p' to each side of the equation. 5m + -2p + 2p = 0 + 2p Combine like terms: -2p + 2p = 0 5m + 0 = 0 + 2p 5m = 0 + 2p Remove the zero: 5m = 2p Divide each side by '5'. m = 0.4p Simplifying m = 0.4pSubproblem 2
Set the factor '(2m + 9p)' equal to zero and attempt to solve: Simplifying 2m + 9p = 0 Solving 2m + 9p = 0 Move all terms containing m to the left, all other terms to the right. Add '-9p' to each side of the equation. 2m + 9p + -9p = 0 + -9p Combine like terms: 9p + -9p = 0 2m + 0 = 0 + -9p 2m = 0 + -9p Remove the zero: 2m = -9p Divide each side by '2'. m = -4.5p Simplifying m = -4.5pSolution
m = {0.4p, -4.5p}
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