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Simplifying 7m2 + -2m = 10 Reorder the terms: -2m + 7m2 = 10 Solving -2m + 7m2 = 10 Solving for variable 'm'. Reorder the terms: -10 + -2m + 7m2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -2m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -0.2857142857m + m2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.2857142857m + 1.428571429 + m2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.2857142857m + m2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.2857142857m + m2 = 0 + 1.428571429 -0.2857142857m + m2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.2857142857m + m2 = 1.428571429 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 = 1.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857m + m2 = 1.428571429 + 0.02040816328 Combine like terms: 1.428571429 + 0.02040816328 = 1.44897959228 0.02040816328 + -0.2857142857m + m2 = 1.44897959228 Factor a perfect square on the left side: (m + -0.1428571429)(m + -0.1428571429) = 1.44897959228 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (m + -0.1428571429) equal to 1.203735682 and -1.203735682.Subproblem 1
m + -0.1428571429 = 1.203735682 Simplifying m + -0.1428571429 = 1.203735682 Reorder the terms: -0.1428571429 + m = 1.203735682 Solving -0.1428571429 + m = 1.203735682 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 = 1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = 1.203735682 + 0.1428571429 m = 1.203735682 + 0.1428571429 Combine like terms: 1.203735682 + 0.1428571429 = 1.3465928249 m = 1.3465928249 Simplifying m = 1.3465928249Subproblem 2
m + -0.1428571429 = -1.203735682 Simplifying m + -0.1428571429 = -1.203735682 Reorder the terms: -0.1428571429 + m = -1.203735682 Solving -0.1428571429 + m = -1.203735682 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 = -1.203735682 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = -1.203735682 + 0.1428571429 m = -1.203735682 + 0.1428571429 Combine like terms: -1.203735682 + 0.1428571429 = -1.0608785391 m = -1.0608785391 Simplifying m = -1.0608785391Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.3465928249, -1.0608785391}
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