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Simplifying 5m2 + -32m + 13 = 0 Reorder the terms: 13 + -32m + 5m2 = 0 Solving 13 + -32m + 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'. 2.6 + -6.4m + m2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -6.4m + -2.6 + m2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -6.4m + m2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -6.4m + m2 = 0 + -2.6 -6.4m + m2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -6.4m + m2 = -2.6 The m term is -6.4m. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4m + 10.24 + m2 = -2.6 + 10.24 Reorder the terms: 10.24 + -6.4m + m2 = -2.6 + 10.24 Combine like terms: -2.6 + 10.24 = 7.64 10.24 + -6.4m + m2 = 7.64 Factor a perfect square on the left side: (m + -3.2)(m + -3.2) = 7.64 Calculate the square root of the right side: 2.764054992 Break this problem into two subproblems by setting (m + -3.2) equal to 2.764054992 and -2.764054992.Subproblem 1
m + -3.2 = 2.764054992 Simplifying m + -3.2 = 2.764054992 Reorder the terms: -3.2 + m = 2.764054992 Solving -3.2 + m = 2.764054992 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + m = 2.764054992 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + m = 2.764054992 + 3.2 m = 2.764054992 + 3.2 Combine like terms: 2.764054992 + 3.2 = 5.964054992 m = 5.964054992 Simplifying m = 5.964054992Subproblem 2
m + -3.2 = -2.764054992 Simplifying m + -3.2 = -2.764054992 Reorder the terms: -3.2 + m = -2.764054992 Solving -3.2 + m = -2.764054992 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + m = -2.764054992 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + m = -2.764054992 + 3.2 m = -2.764054992 + 3.2 Combine like terms: -2.764054992 + 3.2 = 0.435945008 m = 0.435945008 Simplifying m = 0.435945008Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.964054992, 0.435945008}
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