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Simplifying 16m4 + 24m2 + 1 = 0 Reorder the terms: 1 + 24m2 + 16m4 = 0 Solving 1 + 24m2 + 16m4 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + 1.5m2 + m4 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 1.5m2 + -0.0625 + m4 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 1.5m2 + m4 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 1.5m2 + m4 = 0 + -0.0625 1.5m2 + m4 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 1.5m2 + m4 = -0.0625 The m term is 1.5m2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5m2 + 0.5625 + m4 = -0.0625 + 0.5625 Reorder the terms: 0.5625 + 1.5m2 + m4 = -0.0625 + 0.5625 Combine like terms: -0.0625 + 0.5625 = 0.5 0.5625 + 1.5m2 + m4 = 0.5 Factor a perfect square on the left side: (m2 + 0.75)(m2 + 0.75) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (m2 + 0.75) equal to 0.707106781 and -0.707106781.Subproblem 1
m2 + 0.75 = 0.707106781 Simplifying m2 + 0.75 = 0.707106781 Reorder the terms: 0.75 + m2 = 0.707106781 Solving 0.75 + m2 = 0.707106781 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = 0.707106781 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = 0.707106781 + -0.75 m2 = 0.707106781 + -0.75 Combine like terms: 0.707106781 + -0.75 = -0.042893219 m2 = -0.042893219 Simplifying m2 = -0.042893219 Reorder the terms: 0.042893219 + m2 = -0.042893219 + 0.042893219 Combine like terms: -0.042893219 + 0.042893219 = 0.000000000 0.042893219 + 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 + 0.75 = -0.707106781 Simplifying m2 + 0.75 = -0.707106781 Reorder the terms: 0.75 + m2 = -0.707106781 Solving 0.75 + m2 = -0.707106781 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m2 = -0.707106781 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m2 = -0.707106781 + -0.75 m2 = -0.707106781 + -0.75 Combine like terms: -0.707106781 + -0.75 = -1.457106781 m2 = -1.457106781 Simplifying m2 = -1.457106781 Reorder the terms: 1.457106781 + m2 = -1.457106781 + 1.457106781 Combine like terms: -1.457106781 + 1.457106781 = 0.000000000 1.457106781 + 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.
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