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Simplifying 7m2 + 7m + -8 = 0 Reorder the terms: -8 + 7m + 7m2 = 0 Solving -8 + 7m + 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'. -1.142857143 + m + m2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + m + 1.142857143 + m2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + m + m2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + m + m2 = 0 + 1.142857143 m + m2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 m + m2 = 1.142857143 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 1.142857143 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 1.142857143 + 0.25 Combine like terms: 1.142857143 + 0.25 = 1.392857143 1.25 + m2 = 1.392857143 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 1.392857143 Calculate the square root of the right side: 1.180193689 Break this problem into two subproblems by setting (m + 0.5) equal to 1.180193689 and -1.180193689.Subproblem 1
m + 0.5 = 1.180193689 Simplifying m + 0.5 = 1.180193689 Reorder the terms: 0.5 + m = 1.180193689 Solving 0.5 + m = 1.180193689 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.180193689 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.180193689 + -0.5 m = 1.180193689 + -0.5 Combine like terms: 1.180193689 + -0.5 = 0.680193689 m = 0.680193689 Simplifying m = 0.680193689Subproblem 2
m + 0.5 = -1.180193689 Simplifying m + 0.5 = -1.180193689 Reorder the terms: 0.5 + m = -1.180193689 Solving 0.5 + m = -1.180193689 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.180193689 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.180193689 + -0.5 m = -1.180193689 + -0.5 Combine like terms: -1.180193689 + -0.5 = -1.680193689 m = -1.680193689 Simplifying m = -1.680193689Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.680193689, -1.680193689}
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