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Simplifying 16 = 48d + -1d2 Solving 16 = 48d + -1d2 Solving for variable 'd'. Reorder the terms: 16 + -48d + d2 = 48d + -48d + -1d2 + d2 Combine like terms: 48d + -48d = 0 16 + -48d + d2 = 0 + -1d2 + d2 16 + -48d + d2 = -1d2 + d2 Combine like terms: -1d2 + d2 = 0 16 + -48d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -48d + -16 + d2 = 0 + -16 Reorder the terms: 16 + -16 + -48d + d2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -48d + d2 = 0 + -16 -48d + d2 = 0 + -16 Combine like terms: 0 + -16 = -16 -48d + d2 = -16 The d term is -48d. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48d + 576 + d2 = -16 + 576 Reorder the terms: 576 + -48d + d2 = -16 + 576 Combine like terms: -16 + 576 = 560 576 + -48d + d2 = 560 Factor a perfect square on the left side: (d + -24)(d + -24) = 560 Calculate the square root of the right side: 23.664319132 Break this problem into two subproblems by setting (d + -24) equal to 23.664319132 and -23.664319132.Subproblem 1
d + -24 = 23.664319132 Simplifying d + -24 = 23.664319132 Reorder the terms: -24 + d = 23.664319132 Solving -24 + d = 23.664319132 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + d = 23.664319132 + 24 Combine like terms: -24 + 24 = 0 0 + d = 23.664319132 + 24 d = 23.664319132 + 24 Combine like terms: 23.664319132 + 24 = 47.664319132 d = 47.664319132 Simplifying d = 47.664319132Subproblem 2
d + -24 = -23.664319132 Simplifying d + -24 = -23.664319132 Reorder the terms: -24 + d = -23.664319132 Solving -24 + d = -23.664319132 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + d = -23.664319132 + 24 Combine like terms: -24 + 24 = 0 0 + d = -23.664319132 + 24 d = -23.664319132 + 24 Combine like terms: -23.664319132 + 24 = 0.335680868 d = 0.335680868 Simplifying d = 0.335680868Solution
The solution to the problem is based on the solutions from the subproblems. d = {47.664319132, 0.335680868}
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