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Simplifying m2 + 12m = -8 Reorder the terms: 12m + m2 = -8 Solving 12m + m2 = -8 Solving for variable 'm'. Reorder the terms: 8 + 12m + m2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 12m + m2 = 0 Begin completing the square. 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 = -0.708497378 m = -0.708497378 Simplifying m = -0.708497378Subproblem 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 = -11.291502622 m = -11.291502622 Simplifying m = -11.291502622Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.708497378, -11.291502622}
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