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Simplifying 12d2 + -14d + -1 = 0 Reorder the terms: -1 + -14d + 12d2 = 0 Solving -1 + -14d + 12d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + -1.166666667d + d2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -1.166666667d + 0.08333333333 + d2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -1.166666667d + d2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -1.166666667d + d2 = 0 + 0.08333333333 -1.166666667d + d2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -1.166666667d + d2 = 0.08333333333 The d term is -1.166666667d. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667d + 0.3402777780 + d2 = 0.08333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667d + d2 = 0.08333333333 + 0.3402777780 Combine like terms: 0.08333333333 + 0.3402777780 = 0.42361111133 0.3402777780 + -1.166666667d + d2 = 0.42361111133 Factor a perfect square on the left side: (d + -0.5833333335)(d + -0.5833333335) = 0.42361111133 Calculate the square root of the right side: 0.65085414 Break this problem into two subproblems by setting (d + -0.5833333335) equal to 0.65085414 and -0.65085414.Subproblem 1
d + -0.5833333335 = 0.65085414 Simplifying d + -0.5833333335 = 0.65085414 Reorder the terms: -0.5833333335 + d = 0.65085414 Solving -0.5833333335 + d = 0.65085414 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + d = 0.65085414 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + d = 0.65085414 + 0.5833333335 d = 0.65085414 + 0.5833333335 Combine like terms: 0.65085414 + 0.5833333335 = 1.2341874735 d = 1.2341874735 Simplifying d = 1.2341874735Subproblem 2
d + -0.5833333335 = -0.65085414 Simplifying d + -0.5833333335 = -0.65085414 Reorder the terms: -0.5833333335 + d = -0.65085414 Solving -0.5833333335 + d = -0.65085414 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + d = -0.65085414 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + d = -0.65085414 + 0.5833333335 d = -0.65085414 + 0.5833333335 Combine like terms: -0.65085414 + 0.5833333335 = -0.0675208065 d = -0.0675208065 Simplifying d = -0.0675208065Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.2341874735, -0.0675208065}
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