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Simplifying (6m * 6m) + -3m + -11 = 0 Reorder the terms for easier multiplication: (6 * 6m * m) + -3m + -11 = 0 Multiply 6 * 6 (36m * m) + -3m + -11 = 0 Multiply m * m (36m2) + -3m + -11 = 0 Reorder the terms: -11 + -3m + (36m2) = 0 Solving -11 + -3m + (36m2) = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3055555556 + -0.08333333333m + m2 = 0 Move the constant term to the right: Add '0.3055555556' to each side of the equation. -0.3055555556 + -0.08333333333m + 0.3055555556 + m2 = 0 + 0.3055555556 Reorder the terms: -0.3055555556 + 0.3055555556 + -0.08333333333m + m2 = 0 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + -0.08333333333m + m2 = 0 + 0.3055555556 -0.08333333333m + m2 = 0 + 0.3055555556 Combine like terms: 0 + 0.3055555556 = 0.3055555556 -0.08333333333m + m2 = 0.3055555556 The m term is -0.08333333333m. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333m + 0.001736111111 + m2 = 0.3055555556 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333m + m2 = 0.3055555556 + 0.001736111111 Combine like terms: 0.3055555556 + 0.001736111111 = 0.307291666711 0.001736111111 + -0.08333333333m + m2 = 0.307291666711 Factor a perfect square on the left side: ((m) + -0.04166666667)((m) + -0.04166666667) = 0.307291666711 Calculate the square root of the right side: 0.554338946 Break this problem into two subproblems by setting ((m) + -0.04166666667) equal to 0.554338946 and -0.554338946.Subproblem 1
(m) + -0.04166666667 = 0.554338946 Simplifying (m) + -0.04166666667 = 0.554338946 m + -0.04166666667 = 0.554338946 Reorder the terms: -0.04166666667 + m = 0.554338946 Solving -0.04166666667 + m = 0.554338946 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + m = 0.554338946 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + m = 0.554338946 + 0.04166666667 m = 0.554338946 + 0.04166666667 Combine like terms: 0.554338946 + 0.04166666667 = 0.59600561267 m = 0.59600561267 Simplifying m = 0.59600561267Subproblem 2
(m) + -0.04166666667 = -0.554338946 Simplifying (m) + -0.04166666667 = -0.554338946 m + -0.04166666667 = -0.554338946 Reorder the terms: -0.04166666667 + m = -0.554338946 Solving -0.04166666667 + m = -0.554338946 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + m = -0.554338946 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + m = -0.554338946 + 0.04166666667 m = -0.554338946 + 0.04166666667 Combine like terms: -0.554338946 + 0.04166666667 = -0.51267227933 m = -0.51267227933 Simplifying m = -0.51267227933Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.59600561267, -0.51267227933}
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