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Simplifying -0.2d2 + 2.5d + 8 = 0 Reorder the terms: 8 + 2.5d + -0.2d2 = 0 Solving 8 + 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'. -40 + -12.5d + d2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -12.5d + 40 + d2 = 0 + 40 Reorder the terms: -40 + 40 + -12.5d + d2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -12.5d + d2 = 0 + 40 -12.5d + d2 = 0 + 40 Combine like terms: 0 + 40 = 40 -12.5d + d2 = 40 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 = 40 + 39.0625 Reorder the terms: 39.0625 + -12.5d + d2 = 40 + 39.0625 Combine like terms: 40 + 39.0625 = 79.0625 39.0625 + -12.5d + d2 = 79.0625 Factor a perfect square on the left side: (d + -6.25)(d + -6.25) = 79.0625 Calculate the square root of the right side: 8.891709622 Break this problem into two subproblems by setting (d + -6.25) equal to 8.891709622 and -8.891709622.Subproblem 1
d + -6.25 = 8.891709622 Simplifying d + -6.25 = 8.891709622 Reorder the terms: -6.25 + d = 8.891709622 Solving -6.25 + d = 8.891709622 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 = 8.891709622 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + d = 8.891709622 + 6.25 d = 8.891709622 + 6.25 Combine like terms: 8.891709622 + 6.25 = 15.141709622 d = 15.141709622 Simplifying d = 15.141709622Subproblem 2
d + -6.25 = -8.891709622 Simplifying d + -6.25 = -8.891709622 Reorder the terms: -6.25 + d = -8.891709622 Solving -6.25 + d = -8.891709622 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 = -8.891709622 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + d = -8.891709622 + 6.25 d = -8.891709622 + 6.25 Combine like terms: -8.891709622 + 6.25 = -2.641709622 d = -2.641709622 Simplifying d = -2.641709622Solution
The solution to the problem is based on the solutions from the subproblems. d = {15.141709622, -2.641709622}
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