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Simplifying d2 + 4d + -11 = 0 Reorder the terms: -11 + 4d + d2 = 0 Solving -11 + 4d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4d + 11 + d2 = 0 + 11 Reorder the terms: -11 + 11 + 4d + d2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4d + d2 = 0 + 11 4d + d2 = 0 + 11 Combine like terms: 0 + 11 = 11 4d + d2 = 11 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 = 11 + 4 Reorder the terms: 4 + 4d + d2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4d + d2 = 15 Factor a perfect square on the left side: (d + 2)(d + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (d + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
d + 2 = 3.872983346 Simplifying d + 2 = 3.872983346 Reorder the terms: 2 + d = 3.872983346 Solving 2 + d = 3.872983346 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 = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + d = 3.872983346 + -2 d = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 d = 1.872983346 Simplifying d = 1.872983346Subproblem 2
d + 2 = -3.872983346 Simplifying d + 2 = -3.872983346 Reorder the terms: 2 + d = -3.872983346 Solving 2 + d = -3.872983346 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 = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + d = -3.872983346 + -2 d = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 d = -5.872983346 Simplifying d = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.872983346, -5.872983346}
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