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Simplifying d2 + -4d + -27 = 0 Reorder the terms: -27 + -4d + d2 = 0 Solving -27 + -4d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -4d + 27 + d2 = 0 + 27 Reorder the terms: -27 + 27 + -4d + d2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -4d + d2 = 0 + 27 -4d + d2 = 0 + 27 Combine like terms: 0 + 27 = 27 -4d + d2 = 27 The d term is -4d. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4d + 4 + d2 = 27 + 4 Reorder the terms: 4 + -4d + d2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + -4d + d2 = 31 Factor a perfect square on the left side: (d + -2)(d + -2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (d + -2) equal to 5.567764363 and -5.567764363.Subproblem 1
d + -2 = 5.567764363 Simplifying d + -2 = 5.567764363 Reorder the terms: -2 + d = 5.567764363 Solving -2 + d = 5.567764363 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + d = 5.567764363 + 2 d = 5.567764363 + 2 Combine like terms: 5.567764363 + 2 = 7.567764363 d = 7.567764363 Simplifying d = 7.567764363Subproblem 2
d + -2 = -5.567764363 Simplifying d + -2 = -5.567764363 Reorder the terms: -2 + d = -5.567764363 Solving -2 + d = -5.567764363 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = -5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + d = -5.567764363 + 2 d = -5.567764363 + 2 Combine like terms: -5.567764363 + 2 = -3.567764363 d = -3.567764363 Simplifying d = -3.567764363Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.567764363, -3.567764363}
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