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Simplifying 3 * 3 = d(9 + d) Multiply 3 * 3 9 = d(9 + d) 9 = (9 * d + d * d) 9 = (9d + d2) Solving 9 = 9d + d2 Solving for variable 'd'. Reorder the terms: 9 + -9d + -1d2 = 9d + -9d + d2 + -1d2 Combine like terms: 9d + -9d = 0 9 + -9d + -1d2 = 0 + d2 + -1d2 9 + -9d + -1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 9 + -9d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 9d + d2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 9d + 9 + d2 = 0 + 9 Reorder the terms: -9 + 9 + 9d + d2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 9d + d2 = 0 + 9 9d + d2 = 0 + 9 Combine like terms: 0 + 9 = 9 9d + d2 = 9 The d term is 9d. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9d + 20.25 + d2 = 9 + 20.25 Reorder the terms: 20.25 + 9d + d2 = 9 + 20.25 Combine like terms: 9 + 20.25 = 29.25 20.25 + 9d + d2 = 29.25 Factor a perfect square on the left side: (d + 4.5)(d + 4.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (d + 4.5) equal to 5.408326913 and -5.408326913.Subproblem 1
d + 4.5 = 5.408326913 Simplifying d + 4.5 = 5.408326913 Reorder the terms: 4.5 + d = 5.408326913 Solving 4.5 + d = 5.408326913 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + d = 5.408326913 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + d = 5.408326913 + -4.5 d = 5.408326913 + -4.5 Combine like terms: 5.408326913 + -4.5 = 0.908326913 d = 0.908326913 Simplifying d = 0.908326913Subproblem 2
d + 4.5 = -5.408326913 Simplifying d + 4.5 = -5.408326913 Reorder the terms: 4.5 + d = -5.408326913 Solving 4.5 + d = -5.408326913 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + d = -5.408326913 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + d = -5.408326913 + -4.5 d = -5.408326913 + -4.5 Combine like terms: -5.408326913 + -4.5 = -9.908326913 d = -9.908326913 Simplifying d = -9.908326913Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.908326913, -9.908326913}
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