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Simplifying 100 = 10d + d2 Solving 100 = 10d + d2 Solving for variable 'd'. Reorder the terms: 100 + -10d + -1d2 = 10d + -10d + d2 + -1d2 Combine like terms: 10d + -10d = 0 100 + -10d + -1d2 = 0 + d2 + -1d2 100 + -10d + -1d2 = d2 + -1d2 Combine like terms: d2 + -1d2 = 0 100 + -10d + -1d2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 10d + d2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 10d + 100 + d2 = 0 + 100 Reorder the terms: -100 + 100 + 10d + d2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 10d + d2 = 0 + 100 10d + d2 = 0 + 100 Combine like terms: 0 + 100 = 100 10d + d2 = 100 The d term is 10d. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10d + 25 + d2 = 100 + 25 Reorder the terms: 25 + 10d + d2 = 100 + 25 Combine like terms: 100 + 25 = 125 25 + 10d + d2 = 125 Factor a perfect square on the left side: (d + 5)(d + 5) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (d + 5) equal to 11.180339887 and -11.180339887.Subproblem 1
d + 5 = 11.180339887 Simplifying d + 5 = 11.180339887 Reorder the terms: 5 + d = 11.180339887 Solving 5 + d = 11.180339887 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = 11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + d = 11.180339887 + -5 d = 11.180339887 + -5 Combine like terms: 11.180339887 + -5 = 6.180339887 d = 6.180339887 Simplifying d = 6.180339887Subproblem 2
d + 5 = -11.180339887 Simplifying d + 5 = -11.180339887 Reorder the terms: 5 + d = -11.180339887 Solving 5 + d = -11.180339887 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + d = -11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + d = -11.180339887 + -5 d = -11.180339887 + -5 Combine like terms: -11.180339887 + -5 = -16.180339887 d = -16.180339887 Simplifying d = -16.180339887Solution
The solution to the problem is based on the solutions from the subproblems. d = {6.180339887, -16.180339887}
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