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Simplifying d2 + -8d + -19 = 0 Reorder the terms: -19 + -8d + d2 = 0 Solving -19 + -8d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -8d + 19 + d2 = 0 + 19 Reorder the terms: -19 + 19 + -8d + d2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -8d + d2 = 0 + 19 -8d + d2 = 0 + 19 Combine like terms: 0 + 19 = 19 -8d + d2 = 19 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 = 19 + 16 Reorder the terms: 16 + -8d + d2 = 19 + 16 Combine like terms: 19 + 16 = 35 16 + -8d + d2 = 35 Factor a perfect square on the left side: (d + -4)(d + -4) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (d + -4) equal to 5.916079783 and -5.916079783.Subproblem 1
d + -4 = 5.916079783 Simplifying d + -4 = 5.916079783 Reorder the terms: -4 + d = 5.916079783 Solving -4 + d = 5.916079783 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 = 5.916079783 + 4 Combine like terms: -4 + 4 = 0 0 + d = 5.916079783 + 4 d = 5.916079783 + 4 Combine like terms: 5.916079783 + 4 = 9.916079783 d = 9.916079783 Simplifying d = 9.916079783Subproblem 2
d + -4 = -5.916079783 Simplifying d + -4 = -5.916079783 Reorder the terms: -4 + d = -5.916079783 Solving -4 + d = -5.916079783 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 = -5.916079783 + 4 Combine like terms: -4 + 4 = 0 0 + d = -5.916079783 + 4 d = -5.916079783 + 4 Combine like terms: -5.916079783 + 4 = -1.916079783 d = -1.916079783 Simplifying d = -1.916079783Solution
The solution to the problem is based on the solutions from the subproblems. d = {9.916079783, -1.916079783}
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