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Simplifying (3m4 + 4m2 + -8) + (2m2 + 3m4 + -3) = 0 Reorder the terms: (-8 + 4m2 + 3m4) + (2m2 + 3m4 + -3) = 0 Remove parenthesis around (-8 + 4m2 + 3m4) -8 + 4m2 + 3m4 + (2m2 + 3m4 + -3) = 0 Reorder the terms: -8 + 4m2 + 3m4 + (-3 + 2m2 + 3m4) = 0 Remove parenthesis around (-3 + 2m2 + 3m4) -8 + 4m2 + 3m4 + -3 + 2m2 + 3m4 = 0 Reorder the terms: -8 + -3 + 4m2 + 2m2 + 3m4 + 3m4 = 0 Combine like terms: -8 + -3 = -11 -11 + 4m2 + 2m2 + 3m4 + 3m4 = 0 Combine like terms: 4m2 + 2m2 = 6m2 -11 + 6m2 + 3m4 + 3m4 = 0 Combine like terms: 3m4 + 3m4 = 6m4 -11 + 6m2 + 6m4 = 0 Solving -11 + 6m2 + 6m4 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + m2 + m4 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + m2 + 1.833333333 + m4 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + m2 + m4 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + m2 + m4 = 0 + 1.833333333 m2 + m4 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 m2 + m4 = 1.833333333 The m term is m2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m4 = 1.833333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m4 = 1.833333333 + 0.25 Combine like terms: 1.833333333 + 0.25 = 2.083333333 1.25 + m4 = 2.083333333 Factor a perfect square on the left side: (m2 + 0.5)(m2 + 0.5) = 2.083333333 Calculate the square root of the right side: 1.443375673 Break this problem into two subproblems by setting (m2 + 0.5) equal to 1.443375673 and -1.443375673.Subproblem 1
m2 + 0.5 = 1.443375673 Simplifying m2 + 0.5 = 1.443375673 Reorder the terms: 0.5 + m2 = 1.443375673 Solving 0.5 + m2 = 1.443375673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m2 = 1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m2 = 1.443375673 + -0.5 m2 = 1.443375673 + -0.5 Combine like terms: 1.443375673 + -0.5 = 0.943375673 m2 = 0.943375673 Simplifying m2 = 0.943375673 Take the square root of each side: m = {-0.971275282, 0.971275282}Subproblem 2
m2 + 0.5 = -1.443375673 Simplifying m2 + 0.5 = -1.443375673 Reorder the terms: 0.5 + m2 = -1.443375673 Solving 0.5 + m2 = -1.443375673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m2 = -1.443375673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m2 = -1.443375673 + -0.5 m2 = -1.443375673 + -0.5 Combine like terms: -1.443375673 + -0.5 = -1.943375673 m2 = -1.943375673 Simplifying m2 = -1.943375673 Reorder the terms: 1.943375673 + m2 = -1.943375673 + 1.943375673 Combine like terms: -1.943375673 + 1.943375673 = 0.000000000 1.943375673 + 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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