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Simplifying -1.4m + 0.1 = -4.9m2 Reorder the terms: 0.1 + -1.4m = -4.9m2 Solving 0.1 + -1.4m = -4.9m2 Solving for variable 'm'. Combine like terms: -4.9m2 + 4.9m2 = 0.0 0.1 + -1.4m + 4.9m2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.02040816327 + -0.2857142857m + m2 = 0 Move the constant term to the right: Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.2857142857m + -0.02040816327 + m2 = 0 + -0.02040816327 Reorder the terms: 0.02040816327 + -0.02040816327 + -0.2857142857m + m2 = 0 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + -0.2857142857m + m2 = 0 + -0.02040816327 -0.2857142857m + m2 = 0 + -0.02040816327 Combine like terms: 0 + -0.02040816327 = -0.02040816327 -0.2857142857m + m2 = -0.02040816327 The m term is -0.2857142857m. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857m + 0.02040816328 + m2 = -0.02040816327 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857m + m2 = -0.02040816327 + 0.02040816328 Combine like terms: -0.02040816327 + 0.02040816328 = 0.00000000001 0.02040816328 + -0.2857142857m + m2 = 0.00000000001 Factor a perfect square on the left side: (m + -0.1428571429)(m + -0.1428571429) = 0.00000000001 Calculate the square root of the right side: 0.000003162 Break this problem into two subproblems by setting (m + -0.1428571429) equal to 0.000003162 and -0.000003162.Subproblem 1
m + -0.1428571429 = 0.000003162 Simplifying m + -0.1428571429 = 0.000003162 Reorder the terms: -0.1428571429 + m = 0.000003162 Solving -0.1428571429 + m = 0.000003162 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + m = 0.000003162 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = 0.000003162 + 0.1428571429 m = 0.000003162 + 0.1428571429 Combine like terms: 0.000003162 + 0.1428571429 = 0.1428603049 m = 0.1428603049 Simplifying m = 0.1428603049Subproblem 2
m + -0.1428571429 = -0.000003162 Simplifying m + -0.1428571429 = -0.000003162 Reorder the terms: -0.1428571429 + m = -0.000003162 Solving -0.1428571429 + m = -0.000003162 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + m = -0.000003162 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = -0.000003162 + 0.1428571429 m = -0.000003162 + 0.1428571429 Combine like terms: -0.000003162 + 0.1428571429 = 0.1428539809 m = 0.1428539809 Simplifying m = 0.1428539809Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1428603049, 0.1428539809}
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