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Simplifying 49m2 + 28m + -4 = 0 Reorder the terms: -4 + 28m + 49m2 = 0 Solving -4 + 28m + 49m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.08163265306 + 0.5714285714m + m2 = 0 Move the constant term to the right: Add '0.08163265306' to each side of the equation. -0.08163265306 + 0.5714285714m + 0.08163265306 + m2 = 0 + 0.08163265306 Reorder the terms: -0.08163265306 + 0.08163265306 + 0.5714285714m + m2 = 0 + 0.08163265306 Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000 0.00000000000 + 0.5714285714m + m2 = 0 + 0.08163265306 0.5714285714m + m2 = 0 + 0.08163265306 Combine like terms: 0 + 0.08163265306 = 0.08163265306 0.5714285714m + m2 = 0.08163265306 The m term is 0.5714285714m. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714m + 0.08163265305 + m2 = 0.08163265306 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714m + m2 = 0.08163265306 + 0.08163265305 Combine like terms: 0.08163265306 + 0.08163265305 = 0.16326530611 0.08163265305 + 0.5714285714m + m2 = 0.16326530611 Factor a perfect square on the left side: (m + 0.2857142857)(m + 0.2857142857) = 0.16326530611 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (m + 0.2857142857) equal to 0.404061018 and -0.404061018.Subproblem 1
m + 0.2857142857 = 0.404061018 Simplifying m + 0.2857142857 = 0.404061018 Reorder the terms: 0.2857142857 + m = 0.404061018 Solving 0.2857142857 + m = 0.404061018 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = 0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = 0.404061018 + -0.2857142857 m = 0.404061018 + -0.2857142857 Combine like terms: 0.404061018 + -0.2857142857 = 0.1183467323 m = 0.1183467323 Simplifying m = 0.1183467323Subproblem 2
m + 0.2857142857 = -0.404061018 Simplifying m + 0.2857142857 = -0.404061018 Reorder the terms: 0.2857142857 + m = -0.404061018 Solving 0.2857142857 + m = -0.404061018 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + m = -0.404061018 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + m = -0.404061018 + -0.2857142857 m = -0.404061018 + -0.2857142857 Combine like terms: -0.404061018 + -0.2857142857 = -0.6897753037 m = -0.6897753037 Simplifying m = -0.6897753037Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1183467323, -0.6897753037}
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