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Simplifying 42m2 + -119m + -24 = 0 Reorder the terms: -24 + -119m + 42m2 = 0 Solving -24 + -119m + 42m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.5714285714 + -2.833333333m + m2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -2.833333333m + 0.5714285714 + m2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -2.833333333m + m2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -2.833333333m + m2 = 0 + 0.5714285714 -2.833333333m + m2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -2.833333333m + m2 = 0.5714285714 The m term is -2.833333333m. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333m + 2.006944445 + m2 = 0.5714285714 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333m + m2 = 0.5714285714 + 2.006944445 Combine like terms: 0.5714285714 + 2.006944445 = 2.5783730164 2.006944445 + -2.833333333m + m2 = 2.5783730164 Factor a perfect square on the left side: (m + -1.416666667)(m + -1.416666667) = 2.5783730164 Calculate the square root of the right side: 1.605731303 Break this problem into two subproblems by setting (m + -1.416666667) equal to 1.605731303 and -1.605731303.Subproblem 1
m + -1.416666667 = 1.605731303 Simplifying m + -1.416666667 = 1.605731303 Reorder the terms: -1.416666667 + m = 1.605731303 Solving -1.416666667 + m = 1.605731303 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + m = 1.605731303 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + m = 1.605731303 + 1.416666667 m = 1.605731303 + 1.416666667 Combine like terms: 1.605731303 + 1.416666667 = 3.02239797 m = 3.02239797 Simplifying m = 3.02239797Subproblem 2
m + -1.416666667 = -1.605731303 Simplifying m + -1.416666667 = -1.605731303 Reorder the terms: -1.416666667 + m = -1.605731303 Solving -1.416666667 + m = -1.605731303 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + m = -1.605731303 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + m = -1.605731303 + 1.416666667 m = -1.605731303 + 1.416666667 Combine like terms: -1.605731303 + 1.416666667 = -0.189064636 m = -0.189064636 Simplifying m = -0.189064636Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.02239797, -0.189064636}
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