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Simplifying 7m2 + 2m = 6 Reorder the terms: 2m + 7m2 = 6 Solving 2m + 7m2 = 6 Solving for variable 'm'. Reorder the terms: -6 + 2m + 7m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 2m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 0.2857142857m + m2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.2857142857m + 0.8571428571 + m2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.2857142857m + m2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.2857142857m + m2 = 0 + 0.8571428571 0.2857142857m + m2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.2857142857m + m2 = 0.8571428571 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 = 0.8571428571 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857m + m2 = 0.8571428571 + 0.02040816328 Combine like terms: 0.8571428571 + 0.02040816328 = 0.87755102038 0.02040816328 + 0.2857142857m + m2 = 0.87755102038 Factor a perfect square on the left side: (m + 0.1428571429)(m + 0.1428571429) = 0.87755102038 Calculate the square root of the right side: 0.936776932 Break this problem into two subproblems by setting (m + 0.1428571429) equal to 0.936776932 and -0.936776932.Subproblem 1
m + 0.1428571429 = 0.936776932 Simplifying m + 0.1428571429 = 0.936776932 Reorder the terms: 0.1428571429 + m = 0.936776932 Solving 0.1428571429 + m = 0.936776932 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 = 0.936776932 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + m = 0.936776932 + -0.1428571429 m = 0.936776932 + -0.1428571429 Combine like terms: 0.936776932 + -0.1428571429 = 0.7939197891 m = 0.7939197891 Simplifying m = 0.7939197891Subproblem 2
m + 0.1428571429 = -0.936776932 Simplifying m + 0.1428571429 = -0.936776932 Reorder the terms: 0.1428571429 + m = -0.936776932 Solving 0.1428571429 + m = -0.936776932 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 = -0.936776932 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + m = -0.936776932 + -0.1428571429 m = -0.936776932 + -0.1428571429 Combine like terms: -0.936776932 + -0.1428571429 = -1.0796340749 m = -1.0796340749 Simplifying m = -1.0796340749Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.7939197891, -1.0796340749}
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