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Simplifying 60m2 + -20 = 7m Reorder the terms: -20 + 60m2 = 7m Solving -20 + 60m2 = 7m Solving for variable 'm'. Reorder the terms: -20 + -7m + 60m2 = 7m + -7m Combine like terms: 7m + -7m = 0 -20 + -7m + 60m2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.3333333333 + -0.1166666667m + m2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.1166666667m + 0.3333333333 + m2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.1166666667m + m2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.1166666667m + m2 = 0 + 0.3333333333 -0.1166666667m + m2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.1166666667m + m2 = 0.3333333333 The m term is -0.1166666667m. Take half its coefficient (-0.05833333335). Square it (0.003402777780) and add it to both sides. Add '0.003402777780' to each side of the equation. -0.1166666667m + 0.003402777780 + m2 = 0.3333333333 + 0.003402777780 Reorder the terms: 0.003402777780 + -0.1166666667m + m2 = 0.3333333333 + 0.003402777780 Combine like terms: 0.3333333333 + 0.003402777780 = 0.33673611108 0.003402777780 + -0.1166666667m + m2 = 0.33673611108 Factor a perfect square on the left side: (m + -0.05833333335)(m + -0.05833333335) = 0.33673611108 Calculate the square root of the right side: 0.580289679 Break this problem into two subproblems by setting (m + -0.05833333335) equal to 0.580289679 and -0.580289679.Subproblem 1
m + -0.05833333335 = 0.580289679 Simplifying m + -0.05833333335 = 0.580289679 Reorder the terms: -0.05833333335 + m = 0.580289679 Solving -0.05833333335 + m = 0.580289679 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05833333335' to each side of the equation. -0.05833333335 + 0.05833333335 + m = 0.580289679 + 0.05833333335 Combine like terms: -0.05833333335 + 0.05833333335 = 0.00000000000 0.00000000000 + m = 0.580289679 + 0.05833333335 m = 0.580289679 + 0.05833333335 Combine like terms: 0.580289679 + 0.05833333335 = 0.63862301235 m = 0.63862301235 Simplifying m = 0.63862301235Subproblem 2
m + -0.05833333335 = -0.580289679 Simplifying m + -0.05833333335 = -0.580289679 Reorder the terms: -0.05833333335 + m = -0.580289679 Solving -0.05833333335 + m = -0.580289679 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05833333335' to each side of the equation. -0.05833333335 + 0.05833333335 + m = -0.580289679 + 0.05833333335 Combine like terms: -0.05833333335 + 0.05833333335 = 0.00000000000 0.00000000000 + m = -0.580289679 + 0.05833333335 m = -0.580289679 + 0.05833333335 Combine like terms: -0.580289679 + 0.05833333335 = -0.52195634565 m = -0.52195634565 Simplifying m = -0.52195634565Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.63862301235, -0.52195634565}
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