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Simplifying 9d2 + -9d + -5 = 0 Reorder the terms: -5 + -9d + 9d2 = 0 Solving -5 + -9d + 9d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -1d + d2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -1d + 0.5555555556 + d2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -1d + d2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -1d + d2 = 0 + 0.5555555556 -1d + d2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -1d + d2 = 0.5555555556 The d term is -1d. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1d + 0.25 + d2 = 0.5555555556 + 0.25 Reorder the terms: 0.25 + -1d + d2 = 0.5555555556 + 0.25 Combine like terms: 0.5555555556 + 0.25 = 0.8055555556 0.25 + -1d + d2 = 0.8055555556 Factor a perfect square on the left side: (d + -0.5)(d + -0.5) = 0.8055555556 Calculate the square root of the right side: 0.897527468 Break this problem into two subproblems by setting (d + -0.5) equal to 0.897527468 and -0.897527468.Subproblem 1
d + -0.5 = 0.897527468 Simplifying d + -0.5 = 0.897527468 Reorder the terms: -0.5 + d = 0.897527468 Solving -0.5 + d = 0.897527468 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = 0.897527468 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = 0.897527468 + 0.5 d = 0.897527468 + 0.5 Combine like terms: 0.897527468 + 0.5 = 1.397527468 d = 1.397527468 Simplifying d = 1.397527468Subproblem 2
d + -0.5 = -0.897527468 Simplifying d + -0.5 = -0.897527468 Reorder the terms: -0.5 + d = -0.897527468 Solving -0.5 + d = -0.897527468 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + d = -0.897527468 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + d = -0.897527468 + 0.5 d = -0.897527468 + 0.5 Combine like terms: -0.897527468 + 0.5 = -0.397527468 d = -0.397527468 Simplifying d = -0.397527468Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.397527468, -0.397527468}
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