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Simplifying 16m4 + -14m2 + 24m6 = 0 Reorder the terms: -14m2 + 16m4 + 24m6 = 0 Solving -14m2 + 16m4 + 24m6 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m2'. 2m2(-7 + 8m2 + 12m4) = 0 Factor a trinomial. 2m2((-7 + -6m2)(1 + -2m2)) = 0 Ignore the factor 2.Subproblem 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 '(-7 + -6m2)' equal to zero and attempt to solve: Simplifying -7 + -6m2 = 0 Solving -7 + -6m2 = 0 Move all terms containing m to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -6m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6m2 = 0 + 7 -6m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6m2 = 7 Divide each side by '-6'. m2 = -1.166666667 Simplifying m2 = -1.166666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -2m2)' equal to zero and attempt to solve: Simplifying 1 + -2m2 = 0 Solving 1 + -2m2 = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2m2 = 0 + -1 -2m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2m2 = -1 Divide each side by '-2'. m2 = 0.5 Simplifying m2 = 0.5 Take the square root of each side: m = {-0.707106781, 0.707106781}Solution
m = {0, -0.707106781, 0.707106781}
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