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Simplifying m2 + -20m + -86 = -9 Reorder the terms: -86 + -20m + m2 = -9 Solving -86 + -20m + m2 = -9 Solving for variable 'm'. Reorder the terms: -86 + 9 + -20m + m2 = -9 + 9 Combine like terms: -86 + 9 = -77 -77 + -20m + m2 = -9 + 9 Combine like terms: -9 + 9 = 0 -77 + -20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -20m + 77 + m2 = 0 + 77 Reorder the terms: -77 + 77 + -20m + m2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -20m + m2 = 0 + 77 -20m + m2 = 0 + 77 Combine like terms: 0 + 77 = 77 -20m + m2 = 77 The m term is -20m. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20m + 100 + m2 = 77 + 100 Reorder the terms: 100 + -20m + m2 = 77 + 100 Combine like terms: 77 + 100 = 177 100 + -20m + m2 = 177 Factor a perfect square on the left side: (m + -10)(m + -10) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (m + -10) equal to 13.304134696 and -13.304134696.Subproblem 1
m + -10 = 13.304134696 Simplifying m + -10 = 13.304134696 Reorder the terms: -10 + m = 13.304134696 Solving -10 + m = 13.304134696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = 13.304134696 + 10 Combine like terms: -10 + 10 = 0 0 + m = 13.304134696 + 10 m = 13.304134696 + 10 Combine like terms: 13.304134696 + 10 = 23.304134696 m = 23.304134696 Simplifying m = 23.304134696Subproblem 2
m + -10 = -13.304134696 Simplifying m + -10 = -13.304134696 Reorder the terms: -10 + m = -13.304134696 Solving -10 + m = -13.304134696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + m = -13.304134696 + 10 Combine like terms: -10 + 10 = 0 0 + m = -13.304134696 + 10 m = -13.304134696 + 10 Combine like terms: -13.304134696 + 10 = -3.304134696 m = -3.304134696 Simplifying m = -3.304134696Solution
The solution to the problem is based on the solutions from the subproblems. m = {23.304134696, -3.304134696}
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