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Simplifying 24m2 + -23m + -11 = 0 Reorder the terms: -11 + -23m + 24m2 = 0 Solving -11 + -23m + 24m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.4583333333 + -0.9583333333m + m2 = 0 Move the constant term to the right: Add '0.4583333333' to each side of the equation. -0.4583333333 + -0.9583333333m + 0.4583333333 + m2 = 0 + 0.4583333333 Reorder the terms: -0.4583333333 + 0.4583333333 + -0.9583333333m + m2 = 0 + 0.4583333333 Combine like terms: -0.4583333333 + 0.4583333333 = 0.0000000000 0.0000000000 + -0.9583333333m + m2 = 0 + 0.4583333333 -0.9583333333m + m2 = 0 + 0.4583333333 Combine like terms: 0 + 0.4583333333 = 0.4583333333 -0.9583333333m + m2 = 0.4583333333 The m term is -0.9583333333m. Take half its coefficient (-0.4791666667). Square it (0.2296006945) and add it to both sides. Add '0.2296006945' to each side of the equation. -0.9583333333m + 0.2296006945 + m2 = 0.4583333333 + 0.2296006945 Reorder the terms: 0.2296006945 + -0.9583333333m + m2 = 0.4583333333 + 0.2296006945 Combine like terms: 0.4583333333 + 0.2296006945 = 0.6879340278 0.2296006945 + -0.9583333333m + m2 = 0.6879340278 Factor a perfect square on the left side: (m + -0.4791666667)(m + -0.4791666667) = 0.6879340278 Calculate the square root of the right side: 0.829417885 Break this problem into two subproblems by setting (m + -0.4791666667) equal to 0.829417885 and -0.829417885.Subproblem 1
m + -0.4791666667 = 0.829417885 Simplifying m + -0.4791666667 = 0.829417885 Reorder the terms: -0.4791666667 + m = 0.829417885 Solving -0.4791666667 + m = 0.829417885 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4791666667' to each side of the equation. -0.4791666667 + 0.4791666667 + m = 0.829417885 + 0.4791666667 Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000 0.0000000000 + m = 0.829417885 + 0.4791666667 m = 0.829417885 + 0.4791666667 Combine like terms: 0.829417885 + 0.4791666667 = 1.3085845517 m = 1.3085845517 Simplifying m = 1.3085845517Subproblem 2
m + -0.4791666667 = -0.829417885 Simplifying m + -0.4791666667 = -0.829417885 Reorder the terms: -0.4791666667 + m = -0.829417885 Solving -0.4791666667 + m = -0.829417885 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4791666667' to each side of the equation. -0.4791666667 + 0.4791666667 + m = -0.829417885 + 0.4791666667 Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000 0.0000000000 + m = -0.829417885 + 0.4791666667 m = -0.829417885 + 0.4791666667 Combine like terms: -0.829417885 + 0.4791666667 = -0.3502512183 m = -0.3502512183 Simplifying m = -0.3502512183Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.3085845517, -0.3502512183}
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