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Simplifying 2m2 + 12m + 5 = 0 Reorder the terms: 5 + 12m + 2m2 = 0 Solving 5 + 12m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 6m + m2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 6m + -2.5 + m2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 6m + m2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 6m + m2 = 0 + -2.5 6m + m2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 6m + m2 = -2.5 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = -2.5 + 9 Reorder the terms: 9 + 6m + m2 = -2.5 + 9 Combine like terms: -2.5 + 9 = 6.5 9 + 6m + m2 = 6.5 Factor a perfect square on the left side: (m + 3)(m + 3) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (m + 3) equal to 2.549509757 and -2.549509757.Subproblem 1
m + 3 = 2.549509757 Simplifying m + 3 = 2.549509757 Reorder the terms: 3 + m = 2.549509757 Solving 3 + m = 2.549509757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + m = 2.549509757 + -3 m = 2.549509757 + -3 Combine like terms: 2.549509757 + -3 = -0.450490243 m = -0.450490243 Simplifying m = -0.450490243Subproblem 2
m + 3 = -2.549509757 Simplifying m + 3 = -2.549509757 Reorder the terms: 3 + m = -2.549509757 Solving 3 + m = -2.549509757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + m = -2.549509757 + -3 m = -2.549509757 + -3 Combine like terms: -2.549509757 + -3 = -5.549509757 m = -5.549509757 Simplifying m = -5.549509757Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.450490243, -5.549509757}
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