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Simplifying 7m2 + -2m = 4 Reorder the terms: -2m + 7m2 = 4 Solving -2m + 7m2 = 4 Solving for variable 'm'. Reorder the terms: -4 + -2m + 7m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -2m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -0.2857142857m + m2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.2857142857m + 0.5714285714 + m2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.2857142857m + m2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.2857142857m + m2 = 0 + 0.5714285714 -0.2857142857m + m2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.2857142857m + m2 = 0.5714285714 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 = 0.5714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857m + m2 = 0.5714285714 + 0.02040816328 Combine like terms: 0.5714285714 + 0.02040816328 = 0.59183673468 0.02040816328 + -0.2857142857m + m2 = 0.59183673468 Factor a perfect square on the left side: (m + -0.1428571429)(m + -0.1428571429) = 0.59183673468 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (m + -0.1428571429) equal to 0.769309258 and -0.769309258.Subproblem 1
m + -0.1428571429 = 0.769309258 Simplifying m + -0.1428571429 = 0.769309258 Reorder the terms: -0.1428571429 + m = 0.769309258 Solving -0.1428571429 + m = 0.769309258 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 = 0.769309258 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = 0.769309258 + 0.1428571429 m = 0.769309258 + 0.1428571429 Combine like terms: 0.769309258 + 0.1428571429 = 0.9121664009 m = 0.9121664009 Simplifying m = 0.9121664009Subproblem 2
m + -0.1428571429 = -0.769309258 Simplifying m + -0.1428571429 = -0.769309258 Reorder the terms: -0.1428571429 + m = -0.769309258 Solving -0.1428571429 + m = -0.769309258 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 = -0.769309258 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + m = -0.769309258 + 0.1428571429 m = -0.769309258 + 0.1428571429 Combine like terms: -0.769309258 + 0.1428571429 = -0.6264521151 m = -0.6264521151 Simplifying m = -0.6264521151Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.9121664009, -0.6264521151}
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