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Simplifying -7d2 + 8d + 6 = 0 Reorder the terms: 6 + 8d + -7d2 = 0 Solving 6 + 8d + -7d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + -1.142857143d + d2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1.142857143d + 0.8571428571 + d2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1.142857143d + d2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1.142857143d + d2 = 0 + 0.8571428571 -1.142857143d + d2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1.142857143d + d2 = 0.8571428571 The d term is -1.142857143d. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143d + 0.3265306123 + d2 = 0.8571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143d + d2 = 0.8571428571 + 0.3265306123 Combine like terms: 0.8571428571 + 0.3265306123 = 1.1836734694 0.3265306123 + -1.142857143d + d2 = 1.1836734694 Factor a perfect square on the left side: (d + -0.5714285715)(d + -0.5714285715) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (d + -0.5714285715) equal to 1.087967587 and -1.087967587.Subproblem 1
d + -0.5714285715 = 1.087967587 Simplifying d + -0.5714285715 = 1.087967587 Reorder the terms: -0.5714285715 + d = 1.087967587 Solving -0.5714285715 + d = 1.087967587 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + d = 1.087967587 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + d = 1.087967587 + 0.5714285715 d = 1.087967587 + 0.5714285715 Combine like terms: 1.087967587 + 0.5714285715 = 1.6593961585 d = 1.6593961585 Simplifying d = 1.6593961585Subproblem 2
d + -0.5714285715 = -1.087967587 Simplifying d + -0.5714285715 = -1.087967587 Reorder the terms: -0.5714285715 + d = -1.087967587 Solving -0.5714285715 + d = -1.087967587 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + d = -1.087967587 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + d = -1.087967587 + 0.5714285715 d = -1.087967587 + 0.5714285715 Combine like terms: -1.087967587 + 0.5714285715 = -0.5165390155 d = -0.5165390155 Simplifying d = -0.5165390155Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.6593961585, -0.5165390155}
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