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Simplifying 18d2 + 71d + 2 = 0 Reorder the terms: 2 + 71d + 18d2 = 0 Solving 2 + 71d + 18d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.1111111111 + 3.944444444d + d2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 3.944444444d + -0.1111111111 + d2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 3.944444444d + d2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 3.944444444d + d2 = 0 + -0.1111111111 3.944444444d + d2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 3.944444444d + d2 = -0.1111111111 The d term is 3.944444444d. Take half its coefficient (1.972222222). Square it (3.889660493) and add it to both sides. Add '3.889660493' to each side of the equation. 3.944444444d + 3.889660493 + d2 = -0.1111111111 + 3.889660493 Reorder the terms: 3.889660493 + 3.944444444d + d2 = -0.1111111111 + 3.889660493 Combine like terms: -0.1111111111 + 3.889660493 = 3.7785493819 3.889660493 + 3.944444444d + d2 = 3.7785493819 Factor a perfect square on the left side: (d + 1.972222222)(d + 1.972222222) = 3.7785493819 Calculate the square root of the right side: 1.943849115 Break this problem into two subproblems by setting (d + 1.972222222) equal to 1.943849115 and -1.943849115.Subproblem 1
d + 1.972222222 = 1.943849115 Simplifying d + 1.972222222 = 1.943849115 Reorder the terms: 1.972222222 + d = 1.943849115 Solving 1.972222222 + d = 1.943849115 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.972222222' to each side of the equation. 1.972222222 + -1.972222222 + d = 1.943849115 + -1.972222222 Combine like terms: 1.972222222 + -1.972222222 = 0.000000000 0.000000000 + d = 1.943849115 + -1.972222222 d = 1.943849115 + -1.972222222 Combine like terms: 1.943849115 + -1.972222222 = -0.028373107 d = -0.028373107 Simplifying d = -0.028373107Subproblem 2
d + 1.972222222 = -1.943849115 Simplifying d + 1.972222222 = -1.943849115 Reorder the terms: 1.972222222 + d = -1.943849115 Solving 1.972222222 + d = -1.943849115 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1.972222222' to each side of the equation. 1.972222222 + -1.972222222 + d = -1.943849115 + -1.972222222 Combine like terms: 1.972222222 + -1.972222222 = 0.000000000 0.000000000 + d = -1.943849115 + -1.972222222 d = -1.943849115 + -1.972222222 Combine like terms: -1.943849115 + -1.972222222 = -3.916071337 d = -3.916071337 Simplifying d = -3.916071337Solution
The solution to the problem is based on the solutions from the subproblems. d = {-0.028373107, -3.916071337}
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