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Simplifying d2 + -20d + 13 = 0 Reorder the terms: 13 + -20d + d2 = 0 Solving 13 + -20d + d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -20d + -13 + d2 = 0 + -13 Reorder the terms: 13 + -13 + -20d + d2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -20d + d2 = 0 + -13 -20d + d2 = 0 + -13 Combine like terms: 0 + -13 = -13 -20d + d2 = -13 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 = -13 + 100 Reorder the terms: 100 + -20d + d2 = -13 + 100 Combine like terms: -13 + 100 = 87 100 + -20d + d2 = 87 Factor a perfect square on the left side: (d + -10)(d + -10) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (d + -10) equal to 9.327379053 and -9.327379053.Subproblem 1
d + -10 = 9.327379053 Simplifying d + -10 = 9.327379053 Reorder the terms: -10 + d = 9.327379053 Solving -10 + d = 9.327379053 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 = 9.327379053 + 10 Combine like terms: -10 + 10 = 0 0 + d = 9.327379053 + 10 d = 9.327379053 + 10 Combine like terms: 9.327379053 + 10 = 19.327379053 d = 19.327379053 Simplifying d = 19.327379053Subproblem 2
d + -10 = -9.327379053 Simplifying d + -10 = -9.327379053 Reorder the terms: -10 + d = -9.327379053 Solving -10 + d = -9.327379053 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 = -9.327379053 + 10 Combine like terms: -10 + 10 = 0 0 + d = -9.327379053 + 10 d = -9.327379053 + 10 Combine like terms: -9.327379053 + 10 = 0.672620947 d = 0.672620947 Simplifying d = 0.672620947Solution
The solution to the problem is based on the solutions from the subproblems. d = {19.327379053, 0.672620947}
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