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Simplifying m2 + 12m = 19 Reorder the terms: 12m + m2 = 19 Solving 12m + m2 = 19 Solving for variable 'm'. Reorder the terms: -19 + 12m + m2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 12m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 12m + 19 + m2 = 0 + 19 Reorder the terms: -19 + 19 + 12m + m2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 12m + m2 = 0 + 19 12m + m2 = 0 + 19 Combine like terms: 0 + 19 = 19 12m + m2 = 19 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 = 19 + 36 Reorder the terms: 36 + 12m + m2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + 12m + m2 = 55 Factor a perfect square on the left side: (m + 6)(m + 6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (m + 6) equal to 7.416198487 and -7.416198487.Subproblem 1
m + 6 = 7.416198487 Simplifying m + 6 = 7.416198487 Reorder the terms: 6 + m = 7.416198487 Solving 6 + m = 7.416198487 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 = 7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + m = 7.416198487 + -6 m = 7.416198487 + -6 Combine like terms: 7.416198487 + -6 = 1.416198487 m = 1.416198487 Simplifying m = 1.416198487Subproblem 2
m + 6 = -7.416198487 Simplifying m + 6 = -7.416198487 Reorder the terms: 6 + m = -7.416198487 Solving 6 + m = -7.416198487 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 = -7.416198487 + -6 Combine like terms: 6 + -6 = 0 0 + m = -7.416198487 + -6 m = -7.416198487 + -6 Combine like terms: -7.416198487 + -6 = -13.416198487 m = -13.416198487 Simplifying m = -13.416198487Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.416198487, -13.416198487}
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