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Simplifying d2 + -20d = -21 Reorder the terms: -20d + d2 = -21 Solving -20d + d2 = -21 Solving for variable 'd'. Reorder the terms: 21 + -20d + d2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -20d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -20d + -21 + d2 = 0 + -21 Reorder the terms: 21 + -21 + -20d + d2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -20d + d2 = 0 + -21 -20d + d2 = 0 + -21 Combine like terms: 0 + -21 = -21 -20d + d2 = -21 The d term is -20d. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20d + 100 + d2 = -21 + 100 Reorder the terms: 100 + -20d + d2 = -21 + 100 Combine like terms: -21 + 100 = 79 100 + -20d + d2 = 79 Factor a perfect square on the left side: (d + -10)(d + -10) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (d + -10) equal to 8.888194417 and -8.888194417.Subproblem 1
d + -10 = 8.888194417 Simplifying d + -10 = 8.888194417 Reorder the terms: -10 + d = 8.888194417 Solving -10 + d = 8.888194417 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + d = 8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + d = 8.888194417 + 10 d = 8.888194417 + 10 Combine like terms: 8.888194417 + 10 = 18.888194417 d = 18.888194417 Simplifying d = 18.888194417Subproblem 2
d + -10 = -8.888194417 Simplifying d + -10 = -8.888194417 Reorder the terms: -10 + d = -8.888194417 Solving -10 + d = -8.888194417 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + d = -8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + d = -8.888194417 + 10 d = -8.888194417 + 10 Combine like terms: -8.888194417 + 10 = 1.111805583 d = 1.111805583 Simplifying d = 1.111805583Solution
The solution to the problem is based on the solutions from the subproblems. d = {18.888194417, 1.111805583}
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