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Simplifying 2d2 + -18d + -7 = 0 Reorder the terms: -7 + -18d + 2d2 = 0 Solving -7 + -18d + 2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -9d + d2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -9d + 3.5 + d2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -9d + d2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -9d + d2 = 0 + 3.5 -9d + d2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -9d + d2 = 3.5 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 = 3.5 + 20.25 Reorder the terms: 20.25 + -9d + d2 = 3.5 + 20.25 Combine like terms: 3.5 + 20.25 = 23.75 20.25 + -9d + d2 = 23.75 Factor a perfect square on the left side: (d + -4.5)(d + -4.5) = 23.75 Calculate the square root of the right side: 4.873397172 Break this problem into two subproblems by setting (d + -4.5) equal to 4.873397172 and -4.873397172.Subproblem 1
d + -4.5 = 4.873397172 Simplifying d + -4.5 = 4.873397172 Reorder the terms: -4.5 + d = 4.873397172 Solving -4.5 + d = 4.873397172 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 = 4.873397172 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = 4.873397172 + 4.5 d = 4.873397172 + 4.5 Combine like terms: 4.873397172 + 4.5 = 9.373397172 d = 9.373397172 Simplifying d = 9.373397172Subproblem 2
d + -4.5 = -4.873397172 Simplifying d + -4.5 = -4.873397172 Reorder the terms: -4.5 + d = -4.873397172 Solving -4.5 + d = -4.873397172 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 = -4.873397172 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = -4.873397172 + 4.5 d = -4.873397172 + 4.5 Combine like terms: -4.873397172 + 4.5 = -0.373397172 d = -0.373397172 Simplifying d = -0.373397172Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.373397172, -0.373397172}
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