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Simplifying 7m2 + 8m + -3 = 0 Reorder the terms: -3 + 8m + 7m2 = 0 Solving -3 + 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'. -0.4285714286 + 1.142857143m + m2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.142857143m + 0.4285714286 + m2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.142857143m + m2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.142857143m + m2 = 0 + 0.4285714286 1.142857143m + m2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.142857143m + m2 = 0.4285714286 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 = 0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143m + m2 = 0.4285714286 + 0.3265306123 Combine like terms: 0.4285714286 + 0.3265306123 = 0.7551020409 0.3265306123 + 1.142857143m + m2 = 0.7551020409 Factor a perfect square on the left side: (m + 0.5714285715)(m + 0.5714285715) = 0.7551020409 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (m + 0.5714285715) equal to 0.868966076 and -0.868966076.Subproblem 1
m + 0.5714285715 = 0.868966076 Simplifying m + 0.5714285715 = 0.868966076 Reorder the terms: 0.5714285715 + m = 0.868966076 Solving 0.5714285715 + m = 0.868966076 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 = 0.868966076 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = 0.868966076 + -0.5714285715 m = 0.868966076 + -0.5714285715 Combine like terms: 0.868966076 + -0.5714285715 = 0.2975375045 m = 0.2975375045 Simplifying m = 0.2975375045Subproblem 2
m + 0.5714285715 = -0.868966076 Simplifying m + 0.5714285715 = -0.868966076 Reorder the terms: 0.5714285715 + m = -0.868966076 Solving 0.5714285715 + m = -0.868966076 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 = -0.868966076 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + m = -0.868966076 + -0.5714285715 m = -0.868966076 + -0.5714285715 Combine like terms: -0.868966076 + -0.5714285715 = -1.4403946475 m = -1.4403946475 Simplifying m = -1.4403946475Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.2975375045, -1.4403946475}
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