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Simplifying 2m2 + -7m3 + 3m = 0 Reorder the terms: 3m + 2m2 + -7m3 = 0 Solving 3m + 2m2 + -7m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(3 + 2m + -7m2) = 0Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(3 + 2m + -7m2)' equal to zero and attempt to solve: Simplifying 3 + 2m + -7m2 = 0 Solving 3 + 2m + -7m2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.4285714286 + -0.2857142857m + m2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.2857142857m + 0.4285714286 + m2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.2857142857m + m2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.2857142857m + m2 = 0 + 0.4285714286 -0.2857142857m + m2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.2857142857m + m2 = 0.4285714286 The m term is -0.2857142857m. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857m + 0.02040816328 + m2 = 0.4285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857m + m2 = 0.4285714286 + 0.02040816328 Combine like terms: 0.4285714286 + 0.02040816328 = 0.44897959188 0.02040816328 + -0.2857142857m + m2 = 0.44897959188 Factor a perfect square on the left side: (m + -0.1428571429)(m + -0.1428571429) = 0.44897959188 Calculate the square root of the right side: 0.670059394 Break this problem into two subproblems by setting (m + -0.1428571429) equal to 0.670059394 and -0.670059394.Subproblem 1
m + -0.1428571429 = 0.670059394 Simplifying m + -0.1428571429 = 0.670059394 Reorder the terms: -0.1428571429 + m = 0.670059394 Solving -0.1428571429 + m = 0.670059394 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + m = 0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = 0.670059394 + 0.1428571429 m = 0.670059394 + 0.1428571429 Combine like terms: 0.670059394 + 0.1428571429 = 0.8129165369 m = 0.8129165369 Simplifying m = 0.8129165369Subproblem 2
m + -0.1428571429 = -0.670059394 Simplifying m + -0.1428571429 = -0.670059394 Reorder the terms: -0.1428571429 + m = -0.670059394 Solving -0.1428571429 + m = -0.670059394 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + m = -0.670059394 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = -0.670059394 + 0.1428571429 m = -0.670059394 + 0.1428571429 Combine like terms: -0.670059394 + 0.1428571429 = -0.5272022511 m = -0.5272022511 Simplifying m = -0.5272022511Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.8129165369, -0.5272022511}Solution
m = {0, 0.8129165369, -0.5272022511}
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