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Simplifying 40m2 + 170mn + 40n2 = 0 Reorder the terms: 170mn + 40m2 + 40n2 = 0 Solving 170mn + 40m2 + 40n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '10'. 10(17mn + 4m2 + 4n2) = 0 Factor a trinomial. 10((4m + n)(m + 4n)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(4m + n)' equal to zero and attempt to solve: Simplifying 4m + n = 0 Solving 4m + n = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n' to each side of the equation. 4m + n + -1n = 0 + -1n Combine like terms: n + -1n = 0 4m + 0 = 0 + -1n 4m = 0 + -1n Remove the zero: 4m = -1n Divide each side by '4'. m = -0.25n Simplifying m = -0.25nSubproblem 2
Set the factor '(m + 4n)' equal to zero and attempt to solve: Simplifying m + 4n = 0 Solving m + 4n = 0 Move all terms containing m to the left, all other terms to the right. Add '-4n' to each side of the equation. m + 4n + -4n = 0 + -4n Combine like terms: 4n + -4n = 0 m + 0 = 0 + -4n m = 0 + -4n Remove the zero: m = -4n Simplifying m = -4nSolution
m = {-0.25n, -4n}
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