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Simplifying 5d2 + -9d + -3 = 0 Reorder the terms: -3 + -9d + 5d2 = 0 Solving -3 + -9d + 5d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -1.8d + d2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.8d + 0.6 + d2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.8d + d2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.8d + d2 = 0 + 0.6 -1.8d + d2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -1.8d + d2 = 0.6 The d term is -1.8d. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8d + 0.81 + d2 = 0.6 + 0.81 Reorder the terms: 0.81 + -1.8d + d2 = 0.6 + 0.81 Combine like terms: 0.6 + 0.81 = 1.41 0.81 + -1.8d + d2 = 1.41 Factor a perfect square on the left side: (d + -0.9)(d + -0.9) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (d + -0.9) equal to 1.187434209 and -1.187434209.Subproblem 1
d + -0.9 = 1.187434209 Simplifying d + -0.9 = 1.187434209 Reorder the terms: -0.9 + d = 1.187434209 Solving -0.9 + d = 1.187434209 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + d = 1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + d = 1.187434209 + 0.9 d = 1.187434209 + 0.9 Combine like terms: 1.187434209 + 0.9 = 2.087434209 d = 2.087434209 Simplifying d = 2.087434209Subproblem 2
d + -0.9 = -1.187434209 Simplifying d + -0.9 = -1.187434209 Reorder the terms: -0.9 + d = -1.187434209 Solving -0.9 + d = -1.187434209 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + d = -1.187434209 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + d = -1.187434209 + 0.9 d = -1.187434209 + 0.9 Combine like terms: -1.187434209 + 0.9 = -0.287434209 d = -0.287434209 Simplifying d = -0.287434209Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.087434209, -0.287434209}
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