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Simplifying (3M)(M4 + -2M2 + -6) = 0 Remove parenthesis around (3M) 3M(M4 + -2M2 + -6) = 0 Reorder the terms: 3M(-6 + -2M2 + M4) = 0 (-6 * 3M + -2M2 * 3M + M4 * 3M) = 0 (-18M + -6M3 + 3M5) = 0 Solving -18M + -6M3 + 3M5 = 0 Solving for variable 'M'. Factor out the Greatest Common Factor (GCF), '3M'. 3M(-6 + -2M2 + M4) = 0 Ignore the factor 3.Subproblem 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 '(-6 + -2M2 + M4)' equal to zero and attempt to solve: Simplifying -6 + -2M2 + M4 = 0 Solving -6 + -2M2 + M4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2M2 + 6 + M4 = 0 + 6 Reorder the terms: -6 + 6 + -2M2 + M4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2M2 + M4 = 0 + 6 -2M2 + M4 = 0 + 6 Combine like terms: 0 + 6 = 6 -2M2 + M4 = 6 The M term is -2M2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2M2 + 1 + M4 = 6 + 1 Reorder the terms: 1 + -2M2 + M4 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2M2 + M4 = 7 Factor a perfect square on the left side: (M2 + -1)(M2 + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (M2 + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
M2 + -1 = 2.645751311 Simplifying M2 + -1 = 2.645751311 Reorder the terms: -1 + M2 = 2.645751311 Solving -1 + M2 = 2.645751311 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + M2 = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + M2 = 2.645751311 + 1 M2 = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 M2 = 3.645751311 Simplifying M2 = 3.645751311 Take the square root of each side: M = {-1.909385061, 1.909385061}Subproblem 2
M2 + -1 = -2.645751311 Simplifying M2 + -1 = -2.645751311 Reorder the terms: -1 + M2 = -2.645751311 Solving -1 + M2 = -2.645751311 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + M2 = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + M2 = -2.645751311 + 1 M2 = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 M2 = -1.645751311 Simplifying M2 = -1.645751311 Reorder the terms: 1.645751311 + M2 = -1.645751311 + 1.645751311 Combine like terms: -1.645751311 + 1.645751311 = 0.000000000 1.645751311 + M2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
M = {0}
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