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Simplifying m2 + 20m + -85 = -4 Reorder the terms: -85 + 20m + m2 = -4 Solving -85 + 20m + m2 = -4 Solving for variable 'm'. Reorder the terms: -85 + 4 + 20m + m2 = -4 + 4 Combine like terms: -85 + 4 = -81 -81 + 20m + m2 = -4 + 4 Combine like terms: -4 + 4 = 0 -81 + 20m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 20m + 81 + m2 = 0 + 81 Reorder the terms: -81 + 81 + 20m + m2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 20m + m2 = 0 + 81 20m + m2 = 0 + 81 Combine like terms: 0 + 81 = 81 20m + m2 = 81 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 = 81 + 100 Reorder the terms: 100 + 20m + m2 = 81 + 100 Combine like terms: 81 + 100 = 181 100 + 20m + m2 = 181 Factor a perfect square on the left side: (m + 10)(m + 10) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (m + 10) equal to 13.453624047 and -13.453624047.Subproblem 1
m + 10 = 13.453624047 Simplifying m + 10 = 13.453624047 Reorder the terms: 10 + m = 13.453624047 Solving 10 + m = 13.453624047 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 = 13.453624047 + -10 Combine like terms: 10 + -10 = 0 0 + m = 13.453624047 + -10 m = 13.453624047 + -10 Combine like terms: 13.453624047 + -10 = 3.453624047 m = 3.453624047 Simplifying m = 3.453624047Subproblem 2
m + 10 = -13.453624047 Simplifying m + 10 = -13.453624047 Reorder the terms: 10 + m = -13.453624047 Solving 10 + m = -13.453624047 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 = -13.453624047 + -10 Combine like terms: 10 + -10 = 0 0 + m = -13.453624047 + -10 m = -13.453624047 + -10 Combine like terms: -13.453624047 + -10 = -23.453624047 m = -23.453624047 Simplifying m = -23.453624047Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.453624047, -23.453624047}
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