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Simplifying -1m2 + 12m + -8 = 0 Reorder the terms: -8 + 12m + -1m2 = 0 Solving -8 + 12m + -1m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -12m + m2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -12m + -8 + m2 = 0 + -8 Reorder the terms: 8 + -8 + -12m + m2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -12m + m2 = 0 + -8 -12m + m2 = 0 + -8 Combine like terms: 0 + -8 = -8 -12m + m2 = -8 The m term is -12m. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12m + 36 + m2 = -8 + 36 Reorder the terms: 36 + -12m + m2 = -8 + 36 Combine like terms: -8 + 36 = 28 36 + -12m + m2 = 28 Factor a perfect square on the left side: (m + -6)(m + -6) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (m + -6) equal to 5.291502622 and -5.291502622.Subproblem 1
m + -6 = 5.291502622 Simplifying m + -6 = 5.291502622 Reorder the terms: -6 + m = 5.291502622 Solving -6 + m = 5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + m = 5.291502622 + 6 m = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 m = 11.291502622 Simplifying m = 11.291502622Subproblem 2
m + -6 = -5.291502622 Simplifying m + -6 = -5.291502622 Reorder the terms: -6 + m = -5.291502622 Solving -6 + m = -5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + m = -5.291502622 + 6 m = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 m = 0.708497378 Simplifying m = 0.708497378Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.291502622, 0.708497378}
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