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Simplifying 0.77d2 + -1.3d + -9.31 = 12 Reorder the terms: -9.31 + -1.3d + 0.77d2 = 12 Solving -9.31 + -1.3d + 0.77d2 = 12 Solving for variable 'd'. Reorder the terms: -9.31 + -12 + -1.3d + 0.77d2 = 12 + -12 Combine like terms: -9.31 + -12 = -21.31 -21.31 + -1.3d + 0.77d2 = 12 + -12 Combine like terms: 12 + -12 = 0 -21.31 + -1.3d + 0.77d2 = 0 Begin completing the square. Divide all terms by 0.77 the coefficient of the squared term: Divide each side by '0.77'. -27.67532468 + -1.688311688d + d2 = 0 Move the constant term to the right: Add '27.67532468' to each side of the equation. -27.67532468 + -1.688311688d + 27.67532468 + d2 = 0 + 27.67532468 Reorder the terms: -27.67532468 + 27.67532468 + -1.688311688d + d2 = 0 + 27.67532468 Combine like terms: -27.67532468 + 27.67532468 = 0.00000000 0.00000000 + -1.688311688d + d2 = 0 + 27.67532468 -1.688311688d + d2 = 0 + 27.67532468 Combine like terms: 0 + 27.67532468 = 27.67532468 -1.688311688d + d2 = 27.67532468 The d term is -1.688311688d. Take half its coefficient (-0.844155844). Square it (0.7125990890) and add it to both sides. Add '0.7125990890' to each side of the equation. -1.688311688d + 0.7125990890 + d2 = 27.67532468 + 0.7125990890 Reorder the terms: 0.7125990890 + -1.688311688d + d2 = 27.67532468 + 0.7125990890 Combine like terms: 27.67532468 + 0.7125990890 = 28.387923769 0.7125990890 + -1.688311688d + d2 = 28.387923769 Factor a perfect square on the left side: (d + -0.844155844)(d + -0.844155844) = 28.387923769 Calculate the square root of the right side: 5.328031885 Break this problem into two subproblems by setting (d + -0.844155844) equal to 5.328031885 and -5.328031885.Subproblem 1
d + -0.844155844 = 5.328031885 Simplifying d + -0.844155844 = 5.328031885 Reorder the terms: -0.844155844 + d = 5.328031885 Solving -0.844155844 + d = 5.328031885 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.844155844' to each side of the equation. -0.844155844 + 0.844155844 + d = 5.328031885 + 0.844155844 Combine like terms: -0.844155844 + 0.844155844 = 0.000000000 0.000000000 + d = 5.328031885 + 0.844155844 d = 5.328031885 + 0.844155844 Combine like terms: 5.328031885 + 0.844155844 = 6.172187729 d = 6.172187729 Simplifying d = 6.172187729Subproblem 2
d + -0.844155844 = -5.328031885 Simplifying d + -0.844155844 = -5.328031885 Reorder the terms: -0.844155844 + d = -5.328031885 Solving -0.844155844 + d = -5.328031885 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.844155844' to each side of the equation. -0.844155844 + 0.844155844 + d = -5.328031885 + 0.844155844 Combine like terms: -0.844155844 + 0.844155844 = 0.000000000 0.000000000 + d = -5.328031885 + 0.844155844 d = -5.328031885 + 0.844155844 Combine like terms: -5.328031885 + 0.844155844 = -4.483876041 d = -4.483876041 Simplifying d = -4.483876041Solution
The solution to the problem is based on the solutions from the subproblems. d = {6.172187729, -4.483876041}
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