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Simplifying 14m2 + 1 = 6m2 + 7m + 5 Reorder the terms: 1 + 14m2 = 6m2 + 7m + 5 Reorder the terms: 1 + 14m2 = 5 + 7m + 6m2 Solving 1 + 14m2 = 5 + 7m + 6m2 Solving for variable 'm'. Reorder the terms: 1 + -5 + -7m + 14m2 + -6m2 = 5 + 7m + 6m2 + -5 + -7m + -6m2 Combine like terms: 1 + -5 = -4 -4 + -7m + 14m2 + -6m2 = 5 + 7m + 6m2 + -5 + -7m + -6m2 Combine like terms: 14m2 + -6m2 = 8m2 -4 + -7m + 8m2 = 5 + 7m + 6m2 + -5 + -7m + -6m2 Reorder the terms: -4 + -7m + 8m2 = 5 + -5 + 7m + -7m + 6m2 + -6m2 Combine like terms: 5 + -5 = 0 -4 + -7m + 8m2 = 0 + 7m + -7m + 6m2 + -6m2 -4 + -7m + 8m2 = 7m + -7m + 6m2 + -6m2 Combine like terms: 7m + -7m = 0 -4 + -7m + 8m2 = 0 + 6m2 + -6m2 -4 + -7m + 8m2 = 6m2 + -6m2 Combine like terms: 6m2 + -6m2 = 0 -4 + -7m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + -0.875m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.875m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.875m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.875m + m2 = 0 + 0.5 -0.875m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.875m + m2 = 0.5 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 = 0.5 + 0.19140625 Reorder the terms: 0.19140625 + -0.875m + m2 = 0.5 + 0.19140625 Combine like terms: 0.5 + 0.19140625 = 0.69140625 0.19140625 + -0.875m + m2 = 0.69140625 Factor a perfect square on the left side: (m + -0.4375)(m + -0.4375) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (m + -0.4375) equal to 0.831508418 and -0.831508418.Subproblem 1
m + -0.4375 = 0.831508418 Simplifying m + -0.4375 = 0.831508418 Reorder the terms: -0.4375 + m = 0.831508418 Solving -0.4375 + m = 0.831508418 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 = 0.831508418 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = 0.831508418 + 0.4375 m = 0.831508418 + 0.4375 Combine like terms: 0.831508418 + 0.4375 = 1.269008418 m = 1.269008418 Simplifying m = 1.269008418Subproblem 2
m + -0.4375 = -0.831508418 Simplifying m + -0.4375 = -0.831508418 Reorder the terms: -0.4375 + m = -0.831508418 Solving -0.4375 + m = -0.831508418 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 = -0.831508418 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = -0.831508418 + 0.4375 m = -0.831508418 + 0.4375 Combine like terms: -0.831508418 + 0.4375 = -0.394008418 m = -0.394008418 Simplifying m = -0.394008418Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.269008418, -0.394008418}
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