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Simplifying 25m2 + -16 + 9m2 + 49 = 2m2 + -2m + 80 Reorder the terms: -16 + 49 + 25m2 + 9m2 = 2m2 + -2m + 80 Combine like terms: -16 + 49 = 33 33 + 25m2 + 9m2 = 2m2 + -2m + 80 Combine like terms: 25m2 + 9m2 = 34m2 33 + 34m2 = 2m2 + -2m + 80 Reorder the terms: 33 + 34m2 = 80 + -2m + 2m2 Solving 33 + 34m2 = 80 + -2m + 2m2 Solving for variable 'm'. Reorder the terms: 33 + -80 + 2m + 34m2 + -2m2 = 80 + -2m + 2m2 + -80 + 2m + -2m2 Combine like terms: 33 + -80 = -47 -47 + 2m + 34m2 + -2m2 = 80 + -2m + 2m2 + -80 + 2m + -2m2 Combine like terms: 34m2 + -2m2 = 32m2 -47 + 2m + 32m2 = 80 + -2m + 2m2 + -80 + 2m + -2m2 Reorder the terms: -47 + 2m + 32m2 = 80 + -80 + -2m + 2m + 2m2 + -2m2 Combine like terms: 80 + -80 = 0 -47 + 2m + 32m2 = 0 + -2m + 2m + 2m2 + -2m2 -47 + 2m + 32m2 = -2m + 2m + 2m2 + -2m2 Combine like terms: -2m + 2m = 0 -47 + 2m + 32m2 = 0 + 2m2 + -2m2 -47 + 2m + 32m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 -47 + 2m + 32m2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -1.46875 + 0.0625m + m2 = 0 Move the constant term to the right: Add '1.46875' to each side of the equation. -1.46875 + 0.0625m + 1.46875 + m2 = 0 + 1.46875 Reorder the terms: -1.46875 + 1.46875 + 0.0625m + m2 = 0 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + 0.0625m + m2 = 0 + 1.46875 0.0625m + m2 = 0 + 1.46875 Combine like terms: 0 + 1.46875 = 1.46875 0.0625m + m2 = 1.46875 The m term is 0.0625m. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625m + 0.0009765625 + m2 = 1.46875 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625m + m2 = 1.46875 + 0.0009765625 Combine like terms: 1.46875 + 0.0009765625 = 1.4697265625 0.0009765625 + 0.0625m + m2 = 1.4697265625 Factor a perfect square on the left side: (m + 0.03125)(m + 0.03125) = 1.4697265625 Calculate the square root of the right side: 1.212322796 Break this problem into two subproblems by setting (m + 0.03125) equal to 1.212322796 and -1.212322796.Subproblem 1
m + 0.03125 = 1.212322796 Simplifying m + 0.03125 = 1.212322796 Reorder the terms: 0.03125 + m = 1.212322796 Solving 0.03125 + m = 1.212322796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + m = 1.212322796 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + m = 1.212322796 + -0.03125 m = 1.212322796 + -0.03125 Combine like terms: 1.212322796 + -0.03125 = 1.181072796 m = 1.181072796 Simplifying m = 1.181072796Subproblem 2
m + 0.03125 = -1.212322796 Simplifying m + 0.03125 = -1.212322796 Reorder the terms: 0.03125 + m = -1.212322796 Solving 0.03125 + m = -1.212322796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + m = -1.212322796 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + m = -1.212322796 + -0.03125 m = -1.212322796 + -0.03125 Combine like terms: -1.212322796 + -0.03125 = -1.243572796 m = -1.243572796 Simplifying m = -1.243572796Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.181072796, -1.243572796}
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