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Simplifying (12m + -6 + -3m2) + -1(9m2 + 3m + -8) = 0 Reorder the terms: (-6 + 12m + -3m2) + -1(9m2 + 3m + -8) = 0 Remove parenthesis around (-6 + 12m + -3m2) -6 + 12m + -3m2 + -1(9m2 + 3m + -8) = 0 Reorder the terms: -6 + 12m + -3m2 + -1(-8 + 3m + 9m2) = 0 -6 + 12m + -3m2 + (-8 * -1 + 3m * -1 + 9m2 * -1) = 0 -6 + 12m + -3m2 + (8 + -3m + -9m2) = 0 Reorder the terms: -6 + 8 + 12m + -3m + -3m2 + -9m2 = 0 Combine like terms: -6 + 8 = 2 2 + 12m + -3m + -3m2 + -9m2 = 0 Combine like terms: 12m + -3m = 9m 2 + 9m + -3m2 + -9m2 = 0 Combine like terms: -3m2 + -9m2 = -12m2 2 + 9m + -12m2 = 0 Solving 2 + 9m + -12m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.1666666667 + -0.75m + m2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.75m + 0.1666666667 + m2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.75m + m2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.75m + m2 = 0 + 0.1666666667 -0.75m + m2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.75m + m2 = 0.1666666667 The m term is -0.75m. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75m + 0.140625 + m2 = 0.1666666667 + 0.140625 Reorder the terms: 0.140625 + -0.75m + m2 = 0.1666666667 + 0.140625 Combine like terms: 0.1666666667 + 0.140625 = 0.3072916667 0.140625 + -0.75m + m2 = 0.3072916667 Factor a perfect square on the left side: (m + -0.375)(m + -0.375) = 0.3072916667 Calculate the square root of the right side: 0.554338946 Break this problem into two subproblems by setting (m + -0.375) equal to 0.554338946 and -0.554338946.Subproblem 1
m + -0.375 = 0.554338946 Simplifying m + -0.375 = 0.554338946 Reorder the terms: -0.375 + m = 0.554338946 Solving -0.375 + m = 0.554338946 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = 0.554338946 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = 0.554338946 + 0.375 m = 0.554338946 + 0.375 Combine like terms: 0.554338946 + 0.375 = 0.929338946 m = 0.929338946 Simplifying m = 0.929338946Subproblem 2
m + -0.375 = -0.554338946 Simplifying m + -0.375 = -0.554338946 Reorder the terms: -0.375 + m = -0.554338946 Solving -0.375 + m = -0.554338946 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = -0.554338946 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = -0.554338946 + 0.375 m = -0.554338946 + 0.375 Combine like terms: -0.554338946 + 0.375 = -0.179338946 m = -0.179338946 Simplifying m = -0.179338946Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.929338946, -0.179338946}
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