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Simplifying 0 = -0.2d2 + 2d + 0.3 Reorder the terms: 0 = 0.3 + 2d + -0.2d2 Solving 0 = 0.3 + 2d + -0.2d2 Solving for variable 'd'. Combine like terms: 0 + -0.3 = -0.3 -0.3 + -2d + 0.2d2 = 0.3 + 2d + -0.2d2 + -0.3 + -2d + 0.2d2 Reorder the terms: -0.3 + -2d + 0.2d2 = 0.3 + -0.3 + 2d + -2d + -0.2d2 + 0.2d2 Combine like terms: 0.3 + -0.3 = 0.0 -0.3 + -2d + 0.2d2 = 0.0 + 2d + -2d + -0.2d2 + 0.2d2 -0.3 + -2d + 0.2d2 = 2d + -2d + -0.2d2 + 0.2d2 Combine like terms: 2d + -2d = 0 -0.3 + -2d + 0.2d2 = 0 + -0.2d2 + 0.2d2 -0.3 + -2d + 0.2d2 = -0.2d2 + 0.2d2 Combine like terms: -0.2d2 + 0.2d2 = 0.0 -0.3 + -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'. -1.5 + -10d + d2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -10d + 1.5 + d2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -10d + d2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -10d + d2 = 0 + 1.5 -10d + d2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -10d + d2 = 1.5 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 = 1.5 + 25 Reorder the terms: 25 + -10d + d2 = 1.5 + 25 Combine like terms: 1.5 + 25 = 26.5 25 + -10d + d2 = 26.5 Factor a perfect square on the left side: (d + -5)(d + -5) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (d + -5) equal to 5.14781507 and -5.14781507.Subproblem 1
d + -5 = 5.14781507 Simplifying d + -5 = 5.14781507 Reorder the terms: -5 + d = 5.14781507 Solving -5 + d = 5.14781507 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 = 5.14781507 + 5 Combine like terms: -5 + 5 = 0 0 + d = 5.14781507 + 5 d = 5.14781507 + 5 Combine like terms: 5.14781507 + 5 = 10.14781507 d = 10.14781507 Simplifying d = 10.14781507Subproblem 2
d + -5 = -5.14781507 Simplifying d + -5 = -5.14781507 Reorder the terms: -5 + d = -5.14781507 Solving -5 + d = -5.14781507 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 = -5.14781507 + 5 Combine like terms: -5 + 5 = 0 0 + d = -5.14781507 + 5 d = -5.14781507 + 5 Combine like terms: -5.14781507 + 5 = -0.14781507 d = -0.14781507 Simplifying d = -0.14781507Solution
The solution to the problem is based on the solutions from the subproblems. d = {10.14781507, -0.14781507}
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