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Simplifying (-4m2 + m + -10) + (3m + 12 + -7m2) = 0 Reorder the terms: (-10 + m + -4m2) + (3m + 12 + -7m2) = 0 Remove parenthesis around (-10 + m + -4m2) -10 + m + -4m2 + (3m + 12 + -7m2) = 0 Reorder the terms: -10 + m + -4m2 + (12 + 3m + -7m2) = 0 Remove parenthesis around (12 + 3m + -7m2) -10 + m + -4m2 + 12 + 3m + -7m2 = 0 Reorder the terms: -10 + 12 + m + 3m + -4m2 + -7m2 = 0 Combine like terms: -10 + 12 = 2 2 + m + 3m + -4m2 + -7m2 = 0 Combine like terms: m + 3m = 4m 2 + 4m + -4m2 + -7m2 = 0 Combine like terms: -4m2 + -7m2 = -11m2 2 + 4m + -11m2 = 0 Solving 2 + 4m + -11m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.1818181818 + -0.3636363636m + m2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.3636363636m + 0.1818181818 + m2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.3636363636m + m2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.3636363636m + m2 = 0 + 0.1818181818 -0.3636363636m + m2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.3636363636m + m2 = 0.1818181818 The m term is -0.3636363636m. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636m + 0.03305785123 + m2 = 0.1818181818 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636m + m2 = 0.1818181818 + 0.03305785123 Combine like terms: 0.1818181818 + 0.03305785123 = 0.21487603303 0.03305785123 + -0.3636363636m + m2 = 0.21487603303 Factor a perfect square on the left side: (m + -0.1818181818)(m + -0.1818181818) = 0.21487603303 Calculate the square root of the right side: 0.463547228 Break this problem into two subproblems by setting (m + -0.1818181818) equal to 0.463547228 and -0.463547228.Subproblem 1
m + -0.1818181818 = 0.463547228 Simplifying m + -0.1818181818 = 0.463547228 Reorder the terms: -0.1818181818 + m = 0.463547228 Solving -0.1818181818 + m = 0.463547228 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + m = 0.463547228 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + m = 0.463547228 + 0.1818181818 m = 0.463547228 + 0.1818181818 Combine like terms: 0.463547228 + 0.1818181818 = 0.6453654098 m = 0.6453654098 Simplifying m = 0.6453654098Subproblem 2
m + -0.1818181818 = -0.463547228 Simplifying m + -0.1818181818 = -0.463547228 Reorder the terms: -0.1818181818 + m = -0.463547228 Solving -0.1818181818 + m = -0.463547228 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + m = -0.463547228 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + m = -0.463547228 + 0.1818181818 m = -0.463547228 + 0.1818181818 Combine like terms: -0.463547228 + 0.1818181818 = -0.2817290462 m = -0.2817290462 Simplifying m = -0.2817290462Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.6453654098, -0.2817290462}
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