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Simplifying d2 + -17d = 48 Reorder the terms: -17d + d2 = 48 Solving -17d + d2 = 48 Solving for variable 'd'. Reorder the terms: -48 + -17d + d2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -17d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -17d + 48 + d2 = 0 + 48 Reorder the terms: -48 + 48 + -17d + d2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -17d + d2 = 0 + 48 -17d + d2 = 0 + 48 Combine like terms: 0 + 48 = 48 -17d + d2 = 48 The d term is -17d. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17d + 72.25 + d2 = 48 + 72.25 Reorder the terms: 72.25 + -17d + d2 = 48 + 72.25 Combine like terms: 48 + 72.25 = 120.25 72.25 + -17d + d2 = 120.25 Factor a perfect square on the left side: (d + -8.5)(d + -8.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (d + -8.5) equal to 10.9658561 and -10.9658561.Subproblem 1
d + -8.5 = 10.9658561 Simplifying d + -8.5 = 10.9658561 Reorder the terms: -8.5 + d = 10.9658561 Solving -8.5 + d = 10.9658561 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + d = 10.9658561 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + d = 10.9658561 + 8.5 d = 10.9658561 + 8.5 Combine like terms: 10.9658561 + 8.5 = 19.4658561 d = 19.4658561 Simplifying d = 19.4658561Subproblem 2
d + -8.5 = -10.9658561 Simplifying d + -8.5 = -10.9658561 Reorder the terms: -8.5 + d = -10.9658561 Solving -8.5 + d = -10.9658561 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + d = -10.9658561 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + d = -10.9658561 + 8.5 d = -10.9658561 + 8.5 Combine like terms: -10.9658561 + 8.5 = -2.4658561 d = -2.4658561 Simplifying d = -2.4658561Solution
The solution to the problem is based on the solutions from the subproblems. d = {19.4658561, -2.4658561}
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