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Simplifying m(4 + m) + 2(5m + 6) = 0 (4 * m + m * m) + 2(5m + 6) = 0 (4m + m2) + 2(5m + 6) = 0 Reorder the terms: 4m + m2 + 2(6 + 5m) = 0 4m + m2 + (6 * 2 + 5m * 2) = 0 4m + m2 + (12 + 10m) = 0 Reorder the terms: 12 + 4m + 10m + m2 = 0 Combine like terms: 4m + 10m = 14m 12 + 14m + m2 = 0 Solving 12 + 14m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 14m + -12 + m2 = 0 + -12 Reorder the terms: 12 + -12 + 14m + m2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 14m + m2 = 0 + -12 14m + m2 = 0 + -12 Combine like terms: 0 + -12 = -12 14m + m2 = -12 The m term is 14m. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14m + 49 + m2 = -12 + 49 Reorder the terms: 49 + 14m + m2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + 14m + m2 = 37 Factor a perfect square on the left side: (m + 7)(m + 7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (m + 7) equal to 6.08276253 and -6.08276253.Subproblem 1
m + 7 = 6.08276253 Simplifying m + 7 = 6.08276253 Reorder the terms: 7 + m = 6.08276253 Solving 7 + m = 6.08276253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = 6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + m = 6.08276253 + -7 m = 6.08276253 + -7 Combine like terms: 6.08276253 + -7 = -0.91723747 m = -0.91723747 Simplifying m = -0.91723747Subproblem 2
m + 7 = -6.08276253 Simplifying m + 7 = -6.08276253 Reorder the terms: 7 + m = -6.08276253 Solving 7 + m = -6.08276253 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = -6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + m = -6.08276253 + -7 m = -6.08276253 + -7 Combine like terms: -6.08276253 + -7 = -13.08276253 m = -13.08276253 Simplifying m = -13.08276253Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.91723747, -13.08276253}
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