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Simplifying 0.2d2 + -2.2d + 5.6 = 0 Reorder the terms: 5.6 + -2.2d + 0.2d2 = 0 Solving 5.6 + -2.2d + 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'. 28 + -11d + d2 = 0 Move the constant term to the right: Add '-28' to each side of the equation. 28 + -11d + -28 + d2 = 0 + -28 Reorder the terms: 28 + -28 + -11d + d2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -11d + d2 = 0 + -28 -11d + d2 = 0 + -28 Combine like terms: 0 + -28 = -28 -11d + d2 = -28 The d term is -11d. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11d + 30.25 + d2 = -28 + 30.25 Reorder the terms: 30.25 + -11d + d2 = -28 + 30.25 Combine like terms: -28 + 30.25 = 2.25 30.25 + -11d + d2 = 2.25 Factor a perfect square on the left side: (d + -5.5)(d + -5.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (d + -5.5) equal to 1.5 and -1.5.Subproblem 1
d + -5.5 = 1.5 Simplifying d + -5.5 = 1.5 Reorder the terms: -5.5 + d = 1.5 Solving -5.5 + d = 1.5 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + d = 1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + d = 1.5 + 5.5 d = 1.5 + 5.5 Combine like terms: 1.5 + 5.5 = 7 d = 7 Simplifying d = 7Subproblem 2
d + -5.5 = -1.5 Simplifying d + -5.5 = -1.5 Reorder the terms: -5.5 + d = -1.5 Solving -5.5 + d = -1.5 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + d = -1.5 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + d = -1.5 + 5.5 d = -1.5 + 5.5 Combine like terms: -1.5 + 5.5 = 4 d = 4 Simplifying d = 4Solution
The solution to the problem is based on the solutions from the subproblems. d = {7, 4}
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