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Simplifying -0.2d2 + 2.5d + 18.1 = 0 Reorder the terms: 18.1 + 2.5d + -0.2d2 = 0 Solving 18.1 + 2.5d + -0.2d2 = 0 Solving for variable 'd'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -90.5 + -12.5d + d2 = 0 Move the constant term to the right: Add '90.5' to each side of the equation. -90.5 + -12.5d + 90.5 + d2 = 0 + 90.5 Reorder the terms: -90.5 + 90.5 + -12.5d + d2 = 0 + 90.5 Combine like terms: -90.5 + 90.5 = 0.0 0.0 + -12.5d + d2 = 0 + 90.5 -12.5d + d2 = 0 + 90.5 Combine like terms: 0 + 90.5 = 90.5 -12.5d + d2 = 90.5 The d term is -12.5d. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5d + 39.0625 + d2 = 90.5 + 39.0625 Reorder the terms: 39.0625 + -12.5d + d2 = 90.5 + 39.0625 Combine like terms: 90.5 + 39.0625 = 129.5625 39.0625 + -12.5d + d2 = 129.5625 Factor a perfect square on the left side: (d + -6.25)(d + -6.25) = 129.5625 Calculate the square root of the right side: 11.382552438 Break this problem into two subproblems by setting (d + -6.25) equal to 11.382552438 and -11.382552438.Subproblem 1
d + -6.25 = 11.382552438 Simplifying d + -6.25 = 11.382552438 Reorder the terms: -6.25 + d = 11.382552438 Solving -6.25 + d = 11.382552438 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + d = 11.382552438 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + d = 11.382552438 + 6.25 d = 11.382552438 + 6.25 Combine like terms: 11.382552438 + 6.25 = 17.632552438 d = 17.632552438 Simplifying d = 17.632552438Subproblem 2
d + -6.25 = -11.382552438 Simplifying d + -6.25 = -11.382552438 Reorder the terms: -6.25 + d = -11.382552438 Solving -6.25 + d = -11.382552438 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + d = -11.382552438 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + d = -11.382552438 + 6.25 d = -11.382552438 + 6.25 Combine like terms: -11.382552438 + 6.25 = -5.132552438 d = -5.132552438 Simplifying d = -5.132552438Solution
The solution to the problem is based on the solutions from the subproblems. d = {17.632552438, -5.132552438}
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