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Simplifying [(8m2 + 3m + -6) + -1(5m2 + -5m + 9)] + -1(m2 + m + 2) = 0 Reorder the terms: [(-6 + 3m + 8m2) + -1(5m2 + -5m + 9)] + -1(m2 + m + 2) = 0 Remove parenthesis around (-6 + 3m + 8m2) [-6 + 3m + 8m2 + -1(5m2 + -5m + 9)] + -1(m2 + m + 2) = 0 Reorder the terms: [-6 + 3m + 8m2 + -1(9 + -5m + 5m2)] + -1(m2 + m + 2) = 0 [-6 + 3m + 8m2 + (9 * -1 + -5m * -1 + 5m2 * -1)] + -1(m2 + m + 2) = 0 [-6 + 3m + 8m2 + (-9 + 5m + -5m2)] + -1(m2 + m + 2) = 0 Reorder the terms: [-6 + -9 + 3m + 5m + 8m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: -6 + -9 = -15 [-15 + 3m + 5m + 8m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: 3m + 5m = 8m [-15 + 8m + 8m2 + -5m2] + -1(m2 + m + 2) = 0 Combine like terms: 8m2 + -5m2 = 3m2 [-15 + 8m + 3m2] + -1(m2 + m + 2) = 0 Remove brackets around [-15 + 8m + 3m2] -15 + 8m + 3m2 + -1(m2 + m + 2) = 0 Reorder the terms: -15 + 8m + 3m2 + -1(2 + m + m2) = 0 -15 + 8m + 3m2 + (2 * -1 + m * -1 + m2 * -1) = 0 -15 + 8m + 3m2 + (-2 + -1m + -1m2) = 0 Reorder the terms: -15 + -2 + 8m + -1m + 3m2 + -1m2 = 0 Combine like terms: -15 + -2 = -17 -17 + 8m + -1m + 3m2 + -1m2 = 0 Combine like terms: 8m + -1m = 7m -17 + 7m + 3m2 + -1m2 = 0 Combine like terms: 3m2 + -1m2 = 2m2 -17 + 7m + 2m2 = 0 Solving -17 + 7m + 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'. -8.5 + 3.5m + m2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 3.5m + 8.5 + m2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 3.5m + m2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 3.5m + m2 = 0 + 8.5 3.5m + m2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 3.5m + m2 = 8.5 The m term is 3.5m. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5m + 3.0625 + m2 = 8.5 + 3.0625 Reorder the terms: 3.0625 + 3.5m + m2 = 8.5 + 3.0625 Combine like terms: 8.5 + 3.0625 = 11.5625 3.0625 + 3.5m + m2 = 11.5625 Factor a perfect square on the left side: (m + 1.75)(m + 1.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (m + 1.75) equal to 3.400367627 and -3.400367627.Subproblem 1
m + 1.75 = 3.400367627 Simplifying m + 1.75 = 3.400367627 Reorder the terms: 1.75 + m = 3.400367627 Solving 1.75 + m = 3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + m = 3.400367627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + m = 3.400367627 + -1.75 m = 3.400367627 + -1.75 Combine like terms: 3.400367627 + -1.75 = 1.650367627 m = 1.650367627 Simplifying m = 1.650367627Subproblem 2
m + 1.75 = -3.400367627 Simplifying m + 1.75 = -3.400367627 Reorder the terms: 1.75 + m = -3.400367627 Solving 1.75 + m = -3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + m = -3.400367627 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + m = -3.400367627 + -1.75 m = -3.400367627 + -1.75 Combine like terms: -3.400367627 + -1.75 = -5.150367627 m = -5.150367627 Simplifying m = -5.150367627Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.650367627, -5.150367627}
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