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Simplifying d2 + 4d + -29 = 0 Reorder the terms: -29 + 4d + d2 = 0 Solving -29 + 4d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 4d + 29 + d2 = 0 + 29 Reorder the terms: -29 + 29 + 4d + d2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 4d + d2 = 0 + 29 4d + d2 = 0 + 29 Combine like terms: 0 + 29 = 29 4d + d2 = 29 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 = 29 + 4 Reorder the terms: 4 + 4d + d2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + 4d + d2 = 33 Factor a perfect square on the left side: (d + 2)(d + 2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (d + 2) equal to 5.744562647 and -5.744562647.Subproblem 1
d + 2 = 5.744562647 Simplifying d + 2 = 5.744562647 Reorder the terms: 2 + d = 5.744562647 Solving 2 + d = 5.744562647 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 = 5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + d = 5.744562647 + -2 d = 5.744562647 + -2 Combine like terms: 5.744562647 + -2 = 3.744562647 d = 3.744562647 Simplifying d = 3.744562647Subproblem 2
d + 2 = -5.744562647 Simplifying d + 2 = -5.744562647 Reorder the terms: 2 + d = -5.744562647 Solving 2 + d = -5.744562647 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 = -5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + d = -5.744562647 + -2 d = -5.744562647 + -2 Combine like terms: -5.744562647 + -2 = -7.744562647 d = -7.744562647 Simplifying d = -7.744562647Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.744562647, -7.744562647}
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