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Simplifying 14m2 + 1 = 6m2 + 7m Reorder the terms: 1 + 14m2 = 6m2 + 7m Reorder the terms: 1 + 14m2 = 7m + 6m2 Solving 1 + 14m2 = 7m + 6m2 Solving for variable 'm'. Reorder the terms: 1 + -7m + 14m2 + -6m2 = 7m + 6m2 + -7m + -6m2 Combine like terms: 14m2 + -6m2 = 8m2 1 + -7m + 8m2 = 7m + 6m2 + -7m + -6m2 Reorder the terms: 1 + -7m + 8m2 = 7m + -7m + 6m2 + -6m2 Combine like terms: 7m + -7m = 0 1 + -7m + 8m2 = 0 + 6m2 + -6m2 1 + -7m + 8m2 = 6m2 + -6m2 Combine like terms: 6m2 + -6m2 = 0 1 + -7m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -0.875m + m2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -0.875m + -0.125 + m2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -0.875m + m2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -0.875m + m2 = 0 + -0.125 -0.875m + m2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -0.875m + m2 = -0.125 The m term is -0.875m. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875m + 0.19140625 + m2 = -0.125 + 0.19140625 Reorder the terms: 0.19140625 + -0.875m + m2 = -0.125 + 0.19140625 Combine like terms: -0.125 + 0.19140625 = 0.06640625 0.19140625 + -0.875m + m2 = 0.06640625 Factor a perfect square on the left side: (m + -0.4375)(m + -0.4375) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (m + -0.4375) equal to 0.257694102 and -0.257694102.Subproblem 1
m + -0.4375 = 0.257694102 Simplifying m + -0.4375 = 0.257694102 Reorder the terms: -0.4375 + m = 0.257694102 Solving -0.4375 + m = 0.257694102 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = 0.257694102 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = 0.257694102 + 0.4375 m = 0.257694102 + 0.4375 Combine like terms: 0.257694102 + 0.4375 = 0.695194102 m = 0.695194102 Simplifying m = 0.695194102Subproblem 2
m + -0.4375 = -0.257694102 Simplifying m + -0.4375 = -0.257694102 Reorder the terms: -0.4375 + m = -0.257694102 Solving -0.4375 + m = -0.257694102 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = -0.257694102 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = -0.257694102 + 0.4375 m = -0.257694102 + 0.4375 Combine like terms: -0.257694102 + 0.4375 = 0.179805898 m = 0.179805898 Simplifying m = 0.179805898Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.695194102, 0.179805898}
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