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Simplifying 0.5m4 + 3.5m2 + 3 = 0 Reorder the terms: 3 + 3.5m2 + 0.5m4 = 0 Solving 3 + 3.5m2 + 0.5m4 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 6 + 7m2 + m4 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 7m2 + -6 + m4 = 0 + -6 Reorder the terms: 6 + -6 + 7m2 + m4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7m2 + m4 = 0 + -6 7m2 + m4 = 0 + -6 Combine like terms: 0 + -6 = -6 7m2 + m4 = -6 The m term is 7m2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m2 + 12.25 + m4 = -6 + 12.25 Reorder the terms: 12.25 + 7m2 + m4 = -6 + 12.25 Combine like terms: -6 + 12.25 = 6.25 12.25 + 7m2 + m4 = 6.25 Factor a perfect square on the left side: (m2 + 3.5)(m2 + 3.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (m2 + 3.5) equal to 2.5 and -2.5.Subproblem 1
m2 + 3.5 = 2.5 Simplifying m2 + 3.5 = 2.5 Reorder the terms: 3.5 + m2 = 2.5 Solving 3.5 + m2 = 2.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m2 = 2.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m2 = 2.5 + -3.5 m2 = 2.5 + -3.5 Combine like terms: 2.5 + -3.5 = -1 m2 = -1 Simplifying m2 = -1 Reorder the terms: 1 + m2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + m2 = 0 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
m2 + 3.5 = -2.5 Simplifying m2 + 3.5 = -2.5 Reorder the terms: 3.5 + m2 = -2.5 Solving 3.5 + m2 = -2.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m2 = -2.5 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m2 = -2.5 + -3.5 m2 = -2.5 + -3.5 Combine like terms: -2.5 + -3.5 = -6 m2 = -6 Simplifying m2 = -6 Reorder the terms: 6 + m2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + m2 = 0 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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