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Simplifying (8m2 + -7m) + -1(3m2 + 7m + -6) = 0 Reorder the terms: (-7m + 8m2) + -1(3m2 + 7m + -6) = 0 Remove parenthesis around (-7m + 8m2) -7m + 8m2 + -1(3m2 + 7m + -6) = 0 Reorder the terms: -7m + 8m2 + -1(-6 + 7m + 3m2) = 0 -7m + 8m2 + (-6 * -1 + 7m * -1 + 3m2 * -1) = 0 -7m + 8m2 + (6 + -7m + -3m2) = 0 Reorder the terms: 6 + -7m + -7m + 8m2 + -3m2 = 0 Combine like terms: -7m + -7m = -14m 6 + -14m + 8m2 + -3m2 = 0 Combine like terms: 8m2 + -3m2 = 5m2 6 + -14m + 5m2 = 0 Solving 6 + -14m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -2.8m + m2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -2.8m + -1.2 + m2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -2.8m + m2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -2.8m + m2 = 0 + -1.2 -2.8m + m2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -2.8m + m2 = -1.2 The m term is -2.8m. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8m + 1.96 + m2 = -1.2 + 1.96 Reorder the terms: 1.96 + -2.8m + m2 = -1.2 + 1.96 Combine like terms: -1.2 + 1.96 = 0.76 1.96 + -2.8m + m2 = 0.76 Factor a perfect square on the left side: (m + -1.4)(m + -1.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (m + -1.4) equal to 0.871779789 and -0.871779789.Subproblem 1
m + -1.4 = 0.871779789 Simplifying m + -1.4 = 0.871779789 Reorder the terms: -1.4 + m = 0.871779789 Solving -1.4 + m = 0.871779789 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + m = 0.871779789 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + m = 0.871779789 + 1.4 m = 0.871779789 + 1.4 Combine like terms: 0.871779789 + 1.4 = 2.271779789 m = 2.271779789 Simplifying m = 2.271779789Subproblem 2
m + -1.4 = -0.871779789 Simplifying m + -1.4 = -0.871779789 Reorder the terms: -1.4 + m = -0.871779789 Solving -1.4 + m = -0.871779789 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + m = -0.871779789 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + m = -0.871779789 + 1.4 m = -0.871779789 + 1.4 Combine like terms: -0.871779789 + 1.4 = 0.528220211 m = 0.528220211 Simplifying m = 0.528220211Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.271779789, 0.528220211}
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