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Simplifying -2d2 + -16d + 42 = 0 Reorder the terms: 42 + -16d + -2d2 = 0 Solving 42 + -16d + -2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -8d + -1d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -8d + -1d2)' equal to zero and attempt to solve: Simplifying 21 + -8d + -1d2 = 0 Solving 21 + -8d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 8d + d2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 8d + 21 + d2 = 0 + 21 Reorder the terms: -21 + 21 + 8d + d2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8d + d2 = 0 + 21 8d + d2 = 0 + 21 Combine like terms: 0 + 21 = 21 8d + d2 = 21 The d term is 8d. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8d + 16 + d2 = 21 + 16 Reorder the terms: 16 + 8d + d2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8d + d2 = 37 Factor a perfect square on the left side: (d + 4)(d + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (d + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
d + 4 = 6.08276253 Simplifying d + 4 = 6.08276253 Reorder the terms: 4 + d = 6.08276253 Solving 4 + d = 6.08276253 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + d = 6.08276253 + -4 d = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 d = 2.08276253 Simplifying d = 2.08276253Subproblem 2
d + 4 = -6.08276253 Simplifying d + 4 = -6.08276253 Reorder the terms: 4 + d = -6.08276253 Solving 4 + d = -6.08276253 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + d = -6.08276253 + -4 d = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 d = -10.08276253 Simplifying d = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. d = {2.08276253, -10.08276253}Solution
d = {2.08276253, -10.08276253}
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