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Simplifying m2 + 12m + 7 = 0 Reorder the terms: 7 + 12m + m2 = 0 Solving 7 + 12m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 12m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 12m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12m + m2 = 0 + -7 12m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 12m + m2 = -7 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 = -7 + 36 Reorder the terms: 36 + 12m + m2 = -7 + 36 Combine like terms: -7 + 36 = 29 36 + 12m + m2 = 29 Factor a perfect square on the left side: (m + 6)(m + 6) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (m + 6) equal to 5.385164807 and -5.385164807.Subproblem 1
m + 6 = 5.385164807 Simplifying m + 6 = 5.385164807 Reorder the terms: 6 + m = 5.385164807 Solving 6 + m = 5.385164807 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 = 5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + m = 5.385164807 + -6 m = 5.385164807 + -6 Combine like terms: 5.385164807 + -6 = -0.614835193 m = -0.614835193 Simplifying m = -0.614835193Subproblem 2
m + 6 = -5.385164807 Simplifying m + 6 = -5.385164807 Reorder the terms: 6 + m = -5.385164807 Solving 6 + m = -5.385164807 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 = -5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + m = -5.385164807 + -6 m = -5.385164807 + -6 Combine like terms: -5.385164807 + -6 = -11.385164807 m = -11.385164807 Simplifying m = -11.385164807Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.614835193, -11.385164807}
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