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Simplifying 3m6 + 12m4 + m2 = 0 Reorder the terms: m2 + 12m4 + 3m6 = 0 Solving m2 + 12m4 + 3m6 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(1 + 12m2 + 3m4) = 0Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(1 + 12m2 + 3m4)' equal to zero and attempt to solve: Simplifying 1 + 12m2 + 3m4 = 0 Solving 1 + 12m2 + 3m4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 4m2 + m4 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 4m2 + -0.3333333333 + m4 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 4m2 + m4 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 4m2 + m4 = 0 + -0.3333333333 4m2 + m4 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 4m2 + m4 = -0.3333333333 The m term is 4m2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m2 + 4 + m4 = -0.3333333333 + 4 Reorder the terms: 4 + 4m2 + m4 = -0.3333333333 + 4 Combine like terms: -0.3333333333 + 4 = 3.6666666667 4 + 4m2 + m4 = 3.6666666667 Factor a perfect square on the left side: (m2 + 2)(m2 + 2) = 3.6666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (m2 + 2) equal to 1.914854216 and -1.914854216.Subproblem 1
m2 + 2 = 1.914854216 Simplifying m2 + 2 = 1.914854216 Reorder the terms: 2 + m2 = 1.914854216 Solving 2 + m2 = 1.914854216 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m2 = 1.914854216 + -2 Combine like terms: 2 + -2 = 0 0 + m2 = 1.914854216 + -2 m2 = 1.914854216 + -2 Combine like terms: 1.914854216 + -2 = -0.085145784 m2 = -0.085145784 Simplifying m2 = -0.085145784 Reorder the terms: 0.085145784 + m2 = -0.085145784 + 0.085145784 Combine like terms: -0.085145784 + 0.085145784 = 0.000000000 0.085145784 + m2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
m2 + 2 = -1.914854216 Simplifying m2 + 2 = -1.914854216 Reorder the terms: 2 + m2 = -1.914854216 Solving 2 + m2 = -1.914854216 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m2 = -1.914854216 + -2 Combine like terms: 2 + -2 = 0 0 + m2 = -1.914854216 + -2 m2 = -1.914854216 + -2 Combine like terms: -1.914854216 + -2 = -3.914854216 m2 = -3.914854216 Simplifying m2 = -3.914854216 Reorder the terms: 3.914854216 + m2 = -3.914854216 + 3.914854216 Combine like terms: -3.914854216 + 3.914854216 = 0.000000000 3.914854216 + 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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