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Simplifying 7m2 + -8m + -7 = 0 Reorder the terms: -7 + -8m + 7m2 = 0 Solving -7 + -8m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -1.142857143m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.142857143m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -1.142857143m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.142857143m + m2 = 0 + 1 -1.142857143m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.142857143m + m2 = 1 The m term is -1.142857143m. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143m + 0.3265306123 + m2 = 1 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143m + m2 = 1 + 0.3265306123 Combine like terms: 1 + 0.3265306123 = 1.3265306123 0.3265306123 + -1.142857143m + m2 = 1.3265306123 Factor a perfect square on the left side: (m + -0.5714285715)(m + -0.5714285715) = 1.3265306123 Calculate the square root of the right side: 1.151751107 Break this problem into two subproblems by setting (m + -0.5714285715) equal to 1.151751107 and -1.151751107.Subproblem 1
m + -0.5714285715 = 1.151751107 Simplifying m + -0.5714285715 = 1.151751107 Reorder the terms: -0.5714285715 + m = 1.151751107 Solving -0.5714285715 + m = 1.151751107 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + m = 1.151751107 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + m = 1.151751107 + 0.5714285715 m = 1.151751107 + 0.5714285715 Combine like terms: 1.151751107 + 0.5714285715 = 1.7231796785 m = 1.7231796785 Simplifying m = 1.7231796785Subproblem 2
m + -0.5714285715 = -1.151751107 Simplifying m + -0.5714285715 = -1.151751107 Reorder the terms: -0.5714285715 + m = -1.151751107 Solving -0.5714285715 + m = -1.151751107 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + m = -1.151751107 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + m = -1.151751107 + 0.5714285715 m = -1.151751107 + 0.5714285715 Combine like terms: -1.151751107 + 0.5714285715 = -0.5803225355 m = -0.5803225355 Simplifying m = -0.5803225355Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.7231796785, -0.5803225355}
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