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Simplifying 3900d + 326 + -20.22d2 = 0 Reorder the terms: 326 + 3900d + -20.22d2 = 0 Solving 326 + 3900d + -20.22d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -20.22 the coefficient of the squared term: Divide each side by '-20.22'. -16.12265084 + -192.8783383d + d2 = 0 Move the constant term to the right: Add '16.12265084' to each side of the equation. -16.12265084 + -192.8783383d + 16.12265084 + d2 = 0 + 16.12265084 Reorder the terms: -16.12265084 + 16.12265084 + -192.8783383d + d2 = 0 + 16.12265084 Combine like terms: -16.12265084 + 16.12265084 = 0.00000000 0.00000000 + -192.8783383d + d2 = 0 + 16.12265084 -192.8783383d + d2 = 0 + 16.12265084 Combine like terms: 0 + 16.12265084 = 16.12265084 -192.8783383d + d2 = 16.12265084 The d term is -192.8783383d. Take half its coefficient (-96.43916915). Square it (9300.513346) and add it to both sides. Add '9300.513346' to each side of the equation. -192.8783383d + 9300.513346 + d2 = 16.12265084 + 9300.513346 Reorder the terms: 9300.513346 + -192.8783383d + d2 = 16.12265084 + 9300.513346 Combine like terms: 16.12265084 + 9300.513346 = 9316.63599684 9300.513346 + -192.8783383d + d2 = 9316.63599684 Factor a perfect square on the left side: (d + -96.43916915)(d + -96.43916915) = 9316.63599684 Calculate the square root of the right side: 96.522722697 Break this problem into two subproblems by setting (d + -96.43916915) equal to 96.522722697 and -96.522722697.Subproblem 1
d + -96.43916915 = 96.522722697 Simplifying d + -96.43916915 = 96.522722697 Reorder the terms: -96.43916915 + d = 96.522722697 Solving -96.43916915 + d = 96.522722697 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '96.43916915' to each side of the equation. -96.43916915 + 96.43916915 + d = 96.522722697 + 96.43916915 Combine like terms: -96.43916915 + 96.43916915 = 0.00000000 0.00000000 + d = 96.522722697 + 96.43916915 d = 96.522722697 + 96.43916915 Combine like terms: 96.522722697 + 96.43916915 = 192.961891847 d = 192.961891847 Simplifying d = 192.961891847Subproblem 2
d + -96.43916915 = -96.522722697 Simplifying d + -96.43916915 = -96.522722697 Reorder the terms: -96.43916915 + d = -96.522722697 Solving -96.43916915 + d = -96.522722697 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '96.43916915' to each side of the equation. -96.43916915 + 96.43916915 + d = -96.522722697 + 96.43916915 Combine like terms: -96.43916915 + 96.43916915 = 0.00000000 0.00000000 + d = -96.522722697 + 96.43916915 d = -96.522722697 + 96.43916915 Combine like terms: -96.522722697 + 96.43916915 = -0.083553547 d = -0.083553547 Simplifying d = -0.083553547Solution
The solution to the problem is based on the solutions from the subproblems. d = {192.961891847, -0.083553547}
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