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Simplifying -7m(m + 2) = -2m + -2 + -4m Reorder the terms: -7m(2 + m) = -2m + -2 + -4m (2 * -7m + m * -7m) = -2m + -2 + -4m (-14m + -7m2) = -2m + -2 + -4m Reorder the terms: -14m + -7m2 = -2 + -2m + -4m Combine like terms: -2m + -4m = -6m -14m + -7m2 = -2 + -6m Solving -14m + -7m2 = -2 + -6m Solving for variable 'm'. Reorder the terms: 2 + -14m + 6m + -7m2 = -2 + -6m + 2 + 6m Combine like terms: -14m + 6m = -8m 2 + -8m + -7m2 = -2 + -6m + 2 + 6m Reorder the terms: 2 + -8m + -7m2 = -2 + 2 + -6m + 6m Combine like terms: -2 + 2 = 0 2 + -8m + -7m2 = 0 + -6m + 6m 2 + -8m + -7m2 = -6m + 6m Combine like terms: -6m + 6m = 0 2 + -8m + -7m2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.2857142857 + 1.142857143m + m2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.142857143m + 0.2857142857 + m2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.142857143m + m2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.142857143m + m2 = 0 + 0.2857142857 1.142857143m + m2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.142857143m + m2 = 0.2857142857 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 = 0.2857142857 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143m + m2 = 0.2857142857 + 0.3265306123 Combine like terms: 0.2857142857 + 0.3265306123 = 0.612244898 0.3265306123 + 1.142857143m + m2 = 0.612244898 Factor a perfect square on the left side: (m + 0.5714285715)(m + 0.5714285715) = 0.612244898 Calculate the square root of the right side: 0.782460796 Break this problem into two subproblems by setting (m + 0.5714285715) equal to 0.782460796 and -0.782460796.Subproblem 1
m + 0.5714285715 = 0.782460796 Simplifying m + 0.5714285715 = 0.782460796 Reorder the terms: 0.5714285715 + m = 0.782460796 Solving 0.5714285715 + m = 0.782460796 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 = 0.782460796 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = 0.782460796 + -0.5714285715 m = 0.782460796 + -0.5714285715 Combine like terms: 0.782460796 + -0.5714285715 = 0.2110322245 m = 0.2110322245 Simplifying m = 0.2110322245Subproblem 2
m + 0.5714285715 = -0.782460796 Simplifying m + 0.5714285715 = -0.782460796 Reorder the terms: 0.5714285715 + m = -0.782460796 Solving 0.5714285715 + m = -0.782460796 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 = -0.782460796 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = -0.782460796 + -0.5714285715 m = -0.782460796 + -0.5714285715 Combine like terms: -0.782460796 + -0.5714285715 = -1.3538893675 m = -1.3538893675 Simplifying m = -1.3538893675Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.2110322245, -1.3538893675}
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