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Simplifying 1d2 = 18d + -16 Reorder the terms: 1d2 = -16 + 18d Solving 1d2 = -16 + 18d Solving for variable 'd'. Reorder the terms: 16 + -18d + 1d2 = -16 + 18d + 16 + -18d Reorder the terms: 16 + -18d + 1d2 = -16 + 16 + 18d + -18d Combine like terms: -16 + 16 = 0 16 + -18d + 1d2 = 0 + 18d + -18d 16 + -18d + 1d2 = 18d + -18d Combine like terms: 18d + -18d = 0 16 + -18d + 1d2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -18d + -16 + d2 = 0 + -16 Reorder the terms: 16 + -16 + -18d + d2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -18d + d2 = 0 + -16 -18d + d2 = 0 + -16 Combine like terms: 0 + -16 = -16 -18d + d2 = -16 The d term is -18d. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18d + 81 + d2 = -16 + 81 Reorder the terms: 81 + -18d + d2 = -16 + 81 Combine like terms: -16 + 81 = 65 81 + -18d + d2 = 65 Factor a perfect square on the left side: (d + -9)(d + -9) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (d + -9) equal to 8.062257748 and -8.062257748.Subproblem 1
d + -9 = 8.062257748 Simplifying d + -9 = 8.062257748 Reorder the terms: -9 + d = 8.062257748 Solving -9 + d = 8.062257748 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = 8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + d = 8.062257748 + 9 d = 8.062257748 + 9 Combine like terms: 8.062257748 + 9 = 17.062257748 d = 17.062257748 Simplifying d = 17.062257748Subproblem 2
d + -9 = -8.062257748 Simplifying d + -9 = -8.062257748 Reorder the terms: -9 + d = -8.062257748 Solving -9 + d = -8.062257748 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + d = -8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + d = -8.062257748 + 9 d = -8.062257748 + 9 Combine like terms: -8.062257748 + 9 = 0.937742252 d = 0.937742252 Simplifying d = 0.937742252Solution
The solution to the problem is based on the solutions from the subproblems. d = {17.062257748, 0.937742252}
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