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Simplifying m2 + 2m + -48 = 6 Reorder the terms: -48 + 2m + m2 = 6 Solving -48 + 2m + m2 = 6 Solving for variable 'm'. Reorder the terms: -48 + -6 + 2m + m2 = 6 + -6 Combine like terms: -48 + -6 = -54 -54 + 2m + m2 = 6 + -6 Combine like terms: 6 + -6 = 0 -54 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 2m + 54 + m2 = 0 + 54 Reorder the terms: -54 + 54 + 2m + m2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 2m + m2 = 0 + 54 2m + m2 = 0 + 54 Combine like terms: 0 + 54 = 54 2m + m2 = 54 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 54 + 1 Reorder the terms: 1 + 2m + m2 = 54 + 1 Combine like terms: 54 + 1 = 55 1 + 2m + m2 = 55 Factor a perfect square on the left side: (m + 1)(m + 1) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (m + 1) equal to 7.416198487 and -7.416198487.Subproblem 1
m + 1 = 7.416198487 Simplifying m + 1 = 7.416198487 Reorder the terms: 1 + m = 7.416198487 Solving 1 + m = 7.416198487 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + m = 7.416198487 + -1 m = 7.416198487 + -1 Combine like terms: 7.416198487 + -1 = 6.416198487 m = 6.416198487 Simplifying m = 6.416198487Subproblem 2
m + 1 = -7.416198487 Simplifying m + 1 = -7.416198487 Reorder the terms: 1 + m = -7.416198487 Solving 1 + m = -7.416198487 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -7.416198487 + -1 Combine like terms: 1 + -1 = 0 0 + m = -7.416198487 + -1 m = -7.416198487 + -1 Combine like terms: -7.416198487 + -1 = -8.416198487 m = -8.416198487 Simplifying m = -8.416198487Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.416198487, -8.416198487}
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