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Simplifying 9m2 + -19m + 6 = 0 Reorder the terms: 6 + -19m + 9m2 = 0 Solving 6 + -19m + 9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.6666666667 + -2.111111111m + m2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.111111111m + -0.6666666667 + m2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.111111111m + m2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.111111111m + m2 = 0 + -0.6666666667 -2.111111111m + m2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.111111111m + m2 = -0.6666666667 The m term is -2.111111111m. Take half its coefficient (-1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. -2.111111111m + 1.114197532 + m2 = -0.6666666667 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111m + m2 = -0.6666666667 + 1.114197532 Combine like terms: -0.6666666667 + 1.114197532 = 0.4475308653 1.114197532 + -2.111111111m + m2 = 0.4475308653 Factor a perfect square on the left side: (m + -1.055555556)(m + -1.055555556) = 0.4475308653 Calculate the square root of the right side: 0.668977477 Break this problem into two subproblems by setting (m + -1.055555556) equal to 0.668977477 and -0.668977477.Subproblem 1
m + -1.055555556 = 0.668977477 Simplifying m + -1.055555556 = 0.668977477 Reorder the terms: -1.055555556 + m = 0.668977477 Solving -1.055555556 + m = 0.668977477 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + m = 0.668977477 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + m = 0.668977477 + 1.055555556 m = 0.668977477 + 1.055555556 Combine like terms: 0.668977477 + 1.055555556 = 1.724533033 m = 1.724533033 Simplifying m = 1.724533033Subproblem 2
m + -1.055555556 = -0.668977477 Simplifying m + -1.055555556 = -0.668977477 Reorder the terms: -1.055555556 + m = -0.668977477 Solving -1.055555556 + m = -0.668977477 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + m = -0.668977477 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + m = -0.668977477 + 1.055555556 m = -0.668977477 + 1.055555556 Combine like terms: -0.668977477 + 1.055555556 = 0.386578079 m = 0.386578079 Simplifying m = 0.386578079Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.724533033, 0.386578079}
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