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Simplifying 16m2 + -32m = 1 Reorder the terms: -32m + 16m2 = 1 Solving -32m + 16m2 = 1 Solving for variable 'm'. Reorder the terms: -1 + -32m + 16m2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -32m + 16m2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -2m + m2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -2m + 0.0625 + m2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -2m + m2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -2m + m2 = 0 + 0.0625 -2m + m2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -2m + m2 = 0.0625 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 0.0625 + 1 Reorder the terms: 1 + -2m + m2 = 0.0625 + 1 Combine like terms: 0.0625 + 1 = 1.0625 1 + -2m + m2 = 1.0625 Factor a perfect square on the left side: (m + -1)(m + -1) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (m + -1) equal to 1.030776406 and -1.030776406.Subproblem 1
m + -1 = 1.030776406 Simplifying m + -1 = 1.030776406 Reorder the terms: -1 + m = 1.030776406 Solving -1 + m = 1.030776406 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.030776406 + 1 m = 1.030776406 + 1 Combine like terms: 1.030776406 + 1 = 2.030776406 m = 2.030776406 Simplifying m = 2.030776406Subproblem 2
m + -1 = -1.030776406 Simplifying m + -1 = -1.030776406 Reorder the terms: -1 + m = -1.030776406 Solving -1 + m = -1.030776406 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.030776406 + 1 m = -1.030776406 + 1 Combine like terms: -1.030776406 + 1 = -0.030776406 m = -0.030776406 Simplifying m = -0.030776406Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.030776406, -0.030776406}
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