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Simplifying 5m2 + -33m + 13 = 0 Reorder the terms: 13 + -33m + 5m2 = 0 Solving 13 + -33m + 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 + -6.6m + m2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -6.6m + -2.6 + m2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -6.6m + m2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -6.6m + m2 = 0 + -2.6 -6.6m + m2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -6.6m + m2 = -2.6 The m term is -6.6m. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6m + 10.89 + m2 = -2.6 + 10.89 Reorder the terms: 10.89 + -6.6m + m2 = -2.6 + 10.89 Combine like terms: -2.6 + 10.89 = 8.29 10.89 + -6.6m + m2 = 8.29 Factor a perfect square on the left side: (m + -3.3)(m + -3.3) = 8.29 Calculate the square root of the right side: 2.87923601 Break this problem into two subproblems by setting (m + -3.3) equal to 2.87923601 and -2.87923601.Subproblem 1
m + -3.3 = 2.87923601 Simplifying m + -3.3 = 2.87923601 Reorder the terms: -3.3 + m = 2.87923601 Solving -3.3 + m = 2.87923601 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + m = 2.87923601 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + m = 2.87923601 + 3.3 m = 2.87923601 + 3.3 Combine like terms: 2.87923601 + 3.3 = 6.17923601 m = 6.17923601 Simplifying m = 6.17923601Subproblem 2
m + -3.3 = -2.87923601 Simplifying m + -3.3 = -2.87923601 Reorder the terms: -3.3 + m = -2.87923601 Solving -3.3 + m = -2.87923601 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + m = -2.87923601 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + m = -2.87923601 + 3.3 m = -2.87923601 + 3.3 Combine like terms: -2.87923601 + 3.3 = 0.42076399 m = 0.42076399 Simplifying m = 0.42076399Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.17923601, 0.42076399}
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