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Simplifying 4m2 + 12m + 1 = 0 Reorder the terms: 1 + 12m + 4m2 = 0 Solving 1 + 12m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 3m + m2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3m + -0.25 + m2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3m + m2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3m + m2 = 0 + -0.25 3m + m2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3m + m2 = -0.25 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = -0.25 + 2.25 Reorder the terms: 2.25 + 3m + m2 = -0.25 + 2.25 Combine like terms: -0.25 + 2.25 = 2 2.25 + 3m + m2 = 2 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (m + 1.5) equal to 1.414213562 and -1.414213562.Subproblem 1
m + 1.5 = 1.414213562 Simplifying m + 1.5 = 1.414213562 Reorder the terms: 1.5 + m = 1.414213562 Solving 1.5 + m = 1.414213562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 1.414213562 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 1.414213562 + -1.5 m = 1.414213562 + -1.5 Combine like terms: 1.414213562 + -1.5 = -0.085786438 m = -0.085786438 Simplifying m = -0.085786438Subproblem 2
m + 1.5 = -1.414213562 Simplifying m + 1.5 = -1.414213562 Reorder the terms: 1.5 + m = -1.414213562 Solving 1.5 + m = -1.414213562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -1.414213562 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -1.414213562 + -1.5 m = -1.414213562 + -1.5 Combine like terms: -1.414213562 + -1.5 = -2.914213562 m = -2.914213562 Simplifying m = -2.914213562Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.085786438, -2.914213562}
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