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Simplifying [(10m2 + 4m + -1) + -1(7m2 + -2m + 8)] + -1(m2 + m + 9) = 0 Reorder the terms: [(-1 + 4m + 10m2) + -1(7m2 + -2m + 8)] + -1(m2 + m + 9) = 0 Remove parenthesis around (-1 + 4m + 10m2) [-1 + 4m + 10m2 + -1(7m2 + -2m + 8)] + -1(m2 + m + 9) = 0 Reorder the terms: [-1 + 4m + 10m2 + -1(8 + -2m + 7m2)] + -1(m2 + m + 9) = 0 [-1 + 4m + 10m2 + (8 * -1 + -2m * -1 + 7m2 * -1)] + -1(m2 + m + 9) = 0 [-1 + 4m + 10m2 + (-8 + 2m + -7m2)] + -1(m2 + m + 9) = 0 Reorder the terms: [-1 + -8 + 4m + 2m + 10m2 + -7m2] + -1(m2 + m + 9) = 0 Combine like terms: -1 + -8 = -9 [-9 + 4m + 2m + 10m2 + -7m2] + -1(m2 + m + 9) = 0 Combine like terms: 4m + 2m = 6m [-9 + 6m + 10m2 + -7m2] + -1(m2 + m + 9) = 0 Combine like terms: 10m2 + -7m2 = 3m2 [-9 + 6m + 3m2] + -1(m2 + m + 9) = 0 Remove brackets around [-9 + 6m + 3m2] -9 + 6m + 3m2 + -1(m2 + m + 9) = 0 Reorder the terms: -9 + 6m + 3m2 + -1(9 + m + m2) = 0 -9 + 6m + 3m2 + (9 * -1 + m * -1 + m2 * -1) = 0 -9 + 6m + 3m2 + (-9 + -1m + -1m2) = 0 Reorder the terms: -9 + -9 + 6m + -1m + 3m2 + -1m2 = 0 Combine like terms: -9 + -9 = -18 -18 + 6m + -1m + 3m2 + -1m2 = 0 Combine like terms: 6m + -1m = 5m -18 + 5m + 3m2 + -1m2 = 0 Combine like terms: 3m2 + -1m2 = 2m2 -18 + 5m + 2m2 = 0 Solving -18 + 5m + 2m2 = 0 Solving for variable 'm'. Factor a trinomial. (-9 + -2m)(2 + -1m) = 0Subproblem 1
Set the factor '(-9 + -2m)' equal to zero and attempt to solve: Simplifying -9 + -2m = 0 Solving -9 + -2m = 0 Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2m = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2m = 0 + 9 -2m = 0 + 9 Combine like terms: 0 + 9 = 9 -2m = 9 Divide each side by '-2'. m = -4.5 Simplifying m = -4.5Subproblem 2
Set the factor '(2 + -1m)' equal to zero and attempt to solve: Simplifying 2 + -1m = 0 Solving 2 + -1m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1m = 0 + -2 -1m = 0 + -2 Combine like terms: 0 + -2 = -2 -1m = -2 Divide each side by '-1'. m = 2 Simplifying m = 2Solution
m = {-4.5, 2}
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