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Simplifying 16m2 + -1 = 40m Reorder the terms: -1 + 16m2 = 40m Solving -1 + 16m2 = 40m Solving for variable 'm'. Reorder the terms: -1 + -40m + 16m2 = 40m + -40m Combine like terms: 40m + -40m = 0 -1 + -40m + 16m2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -2.5m + m2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -2.5m + 0.0625 + m2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -2.5m + m2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -2.5m + m2 = 0 + 0.0625 -2.5m + m2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -2.5m + m2 = 0.0625 The m term is -2.5m. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5m + 1.5625 + m2 = 0.0625 + 1.5625 Reorder the terms: 1.5625 + -2.5m + m2 = 0.0625 + 1.5625 Combine like terms: 0.0625 + 1.5625 = 1.625 1.5625 + -2.5m + m2 = 1.625 Factor a perfect square on the left side: (m + -1.25)(m + -1.25) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (m + -1.25) equal to 1.274754878 and -1.274754878.Subproblem 1
m + -1.25 = 1.274754878 Simplifying m + -1.25 = 1.274754878 Reorder the terms: -1.25 + m = 1.274754878 Solving -1.25 + m = 1.274754878 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = 1.274754878 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = 1.274754878 + 1.25 m = 1.274754878 + 1.25 Combine like terms: 1.274754878 + 1.25 = 2.524754878 m = 2.524754878 Simplifying m = 2.524754878Subproblem 2
m + -1.25 = -1.274754878 Simplifying m + -1.25 = -1.274754878 Reorder the terms: -1.25 + m = -1.274754878 Solving -1.25 + m = -1.274754878 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + m = -1.274754878 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + m = -1.274754878 + 1.25 m = -1.274754878 + 1.25 Combine like terms: -1.274754878 + 1.25 = -0.024754878 m = -0.024754878 Simplifying m = -0.024754878Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.524754878, -0.024754878}
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