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Simplifying 11m2 + -5m + -9 = 0 Reorder the terms: -9 + -5m + 11m2 = 0 Solving -9 + -5m + 11m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.8181818182 + -0.4545454545m + m2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + -0.4545454545m + 0.8181818182 + m2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + -0.4545454545m + m2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + -0.4545454545m + m2 = 0 + 0.8181818182 -0.4545454545m + m2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 -0.4545454545m + m2 = 0.8181818182 The m term is -0.4545454545m. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545m + 0.05165289257 + m2 = 0.8181818182 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545m + m2 = 0.8181818182 + 0.05165289257 Combine like terms: 0.8181818182 + 0.05165289257 = 0.86983471077 0.05165289257 + -0.4545454545m + m2 = 0.86983471077 Factor a perfect square on the left side: (m + -0.2272727273)(m + -0.2272727273) = 0.86983471077 Calculate the square root of the right side: 0.932649297 Break this problem into two subproblems by setting (m + -0.2272727273) equal to 0.932649297 and -0.932649297.Subproblem 1
m + -0.2272727273 = 0.932649297 Simplifying m + -0.2272727273 = 0.932649297 Reorder the terms: -0.2272727273 + m = 0.932649297 Solving -0.2272727273 + m = 0.932649297 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + m = 0.932649297 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + m = 0.932649297 + 0.2272727273 m = 0.932649297 + 0.2272727273 Combine like terms: 0.932649297 + 0.2272727273 = 1.1599220243 m = 1.1599220243 Simplifying m = 1.1599220243Subproblem 2
m + -0.2272727273 = -0.932649297 Simplifying m + -0.2272727273 = -0.932649297 Reorder the terms: -0.2272727273 + m = -0.932649297 Solving -0.2272727273 + m = -0.932649297 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + m = -0.932649297 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + m = -0.932649297 + 0.2272727273 m = -0.932649297 + 0.2272727273 Combine like terms: -0.932649297 + 0.2272727273 = -0.7053765697 m = -0.7053765697 Simplifying m = -0.7053765697Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.1599220243, -0.7053765697}
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