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Simplifying d2 + 30d = 11 Reorder the terms: 30d + d2 = 11 Solving 30d + d2 = 11 Solving for variable 'd'. Reorder the terms: -11 + 30d + d2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 30d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 30d + 11 + d2 = 0 + 11 Reorder the terms: -11 + 11 + 30d + d2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 30d + d2 = 0 + 11 30d + d2 = 0 + 11 Combine like terms: 0 + 11 = 11 30d + d2 = 11 The d term is 30d. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30d + 225 + d2 = 11 + 225 Reorder the terms: 225 + 30d + d2 = 11 + 225 Combine like terms: 11 + 225 = 236 225 + 30d + d2 = 236 Factor a perfect square on the left side: (d + 15)(d + 15) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (d + 15) equal to 15.362291496 and -15.362291496.Subproblem 1
d + 15 = 15.362291496 Simplifying d + 15 = 15.362291496 Reorder the terms: 15 + d = 15.362291496 Solving 15 + d = 15.362291496 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + d = 15.362291496 + -15 Combine like terms: 15 + -15 = 0 0 + d = 15.362291496 + -15 d = 15.362291496 + -15 Combine like terms: 15.362291496 + -15 = 0.362291496 d = 0.362291496 Simplifying d = 0.362291496Subproblem 2
d + 15 = -15.362291496 Simplifying d + 15 = -15.362291496 Reorder the terms: 15 + d = -15.362291496 Solving 15 + d = -15.362291496 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + d = -15.362291496 + -15 Combine like terms: 15 + -15 = 0 0 + d = -15.362291496 + -15 d = -15.362291496 + -15 Combine like terms: -15.362291496 + -15 = -30.362291496 d = -30.362291496 Simplifying d = -30.362291496Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.362291496, -30.362291496}
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