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Simplifying 2m + 5m(m + 6) = 3m + 14 Reorder the terms: 2m + 5m(6 + m) = 3m + 14 2m + (6 * 5m + m * 5m) = 3m + 14 2m + (30m + 5m2) = 3m + 14 Combine like terms: 2m + 30m = 32m 32m + 5m2 = 3m + 14 Reorder the terms: 32m + 5m2 = 14 + 3m Solving 32m + 5m2 = 14 + 3m Solving for variable 'm'. Reorder the terms: -14 + 32m + -3m + 5m2 = 14 + 3m + -14 + -3m Combine like terms: 32m + -3m = 29m -14 + 29m + 5m2 = 14 + 3m + -14 + -3m Reorder the terms: -14 + 29m + 5m2 = 14 + -14 + 3m + -3m Combine like terms: 14 + -14 = 0 -14 + 29m + 5m2 = 0 + 3m + -3m -14 + 29m + 5m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -14 + 29m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + 5.8m + m2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 5.8m + 2.8 + m2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 5.8m + m2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 5.8m + m2 = 0 + 2.8 5.8m + m2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 5.8m + m2 = 2.8 The m term is 5.8m. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8m + 8.41 + m2 = 2.8 + 8.41 Reorder the terms: 8.41 + 5.8m + m2 = 2.8 + 8.41 Combine like terms: 2.8 + 8.41 = 11.21 8.41 + 5.8m + m2 = 11.21 Factor a perfect square on the left side: (m + 2.9)(m + 2.9) = 11.21 Calculate the square root of the right side: 3.348133809 Break this problem into two subproblems by setting (m + 2.9) equal to 3.348133809 and -3.348133809.Subproblem 1
m + 2.9 = 3.348133809 Simplifying m + 2.9 = 3.348133809 Reorder the terms: 2.9 + m = 3.348133809 Solving 2.9 + m = 3.348133809 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + m = 3.348133809 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + m = 3.348133809 + -2.9 m = 3.348133809 + -2.9 Combine like terms: 3.348133809 + -2.9 = 0.448133809 m = 0.448133809 Simplifying m = 0.448133809Subproblem 2
m + 2.9 = -3.348133809 Simplifying m + 2.9 = -3.348133809 Reorder the terms: 2.9 + m = -3.348133809 Solving 2.9 + m = -3.348133809 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + m = -3.348133809 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + m = -3.348133809 + -2.9 m = -3.348133809 + -2.9 Combine like terms: -3.348133809 + -2.9 = -6.248133809 m = -6.248133809 Simplifying m = -6.248133809Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.448133809, -6.248133809}
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