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Simplifying 25 = 0.2d2 + 2d Reorder the terms: 25 = 2d + 0.2d2 Solving 25 = 2d + 0.2d2 Solving for variable 'd'. Reorder the terms: 25 + -2d + -0.2d2 = 2d + -2d + 0.2d2 + -0.2d2 Combine like terms: 2d + -2d = 0 25 + -2d + -0.2d2 = 0 + 0.2d2 + -0.2d2 25 + -2d + -0.2d2 = 0.2d2 + -0.2d2 Combine like terms: 0.2d2 + -0.2d2 = 0.0 25 + -2d + -0.2d2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -125 + 10d + d2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 10d + 125 + d2 = 0 + 125 Reorder the terms: -125 + 125 + 10d + d2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 10d + d2 = 0 + 125 10d + d2 = 0 + 125 Combine like terms: 0 + 125 = 125 10d + d2 = 125 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 = 125 + 25 Reorder the terms: 25 + 10d + d2 = 125 + 25 Combine like terms: 125 + 25 = 150 25 + 10d + d2 = 150 Factor a perfect square on the left side: (d + 5)(d + 5) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (d + 5) equal to 12.247448714 and -12.247448714.Subproblem 1
d + 5 = 12.247448714 Simplifying d + 5 = 12.247448714 Reorder the terms: 5 + d = 12.247448714 Solving 5 + d = 12.247448714 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 = 12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + d = 12.247448714 + -5 d = 12.247448714 + -5 Combine like terms: 12.247448714 + -5 = 7.247448714 d = 7.247448714 Simplifying d = 7.247448714Subproblem 2
d + 5 = -12.247448714 Simplifying d + 5 = -12.247448714 Reorder the terms: 5 + d = -12.247448714 Solving 5 + d = -12.247448714 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 = -12.247448714 + -5 Combine like terms: 5 + -5 = 0 0 + d = -12.247448714 + -5 d = -12.247448714 + -5 Combine like terms: -12.247448714 + -5 = -17.247448714 d = -17.247448714 Simplifying d = -17.247448714Solution
The solution to the problem is based on the solutions from the subproblems. d = {7.247448714, -17.247448714}
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