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Simplifying (0.39 + -1d)(0.39 + -1d) = 0 Multiply (0.39 + -1d) * (0.39 + -1d) (0.39(0.39 + -1d) + -1d * (0.39 + -1d)) = 0 ((0.39 * 0.39 + -1d * 0.39) + -1d * (0.39 + -1d)) = 0 ((0.1521 + -0.39d) + -1d * (0.39 + -1d)) = 0 (0.1521 + -0.39d + (0.39 * -1d + -1d * -1d)) = 0 (0.1521 + -0.39d + (-0.39d + 1d2)) = 0 Combine like terms: -0.39d + -0.39d = -0.78d (0.1521 + -0.78d + 1d2) = 0 Solving 0.1521 + -0.78d + 1d2 = 0 Solving for variable 'd'. Begin completing the square. Move the constant term to the right: Add '-0.1521' to each side of the equation. 0.1521 + -0.78d + -0.1521 + d2 = 0 + -0.1521 Reorder the terms: 0.1521 + -0.1521 + -0.78d + d2 = 0 + -0.1521 Combine like terms: 0.1521 + -0.1521 = 0.0000 0.0000 + -0.78d + d2 = 0 + -0.1521 -0.78d + d2 = 0 + -0.1521 Combine like terms: 0 + -0.1521 = -0.1521 -0.78d + d2 = -0.1521 The d term is -0.78d. Take half its coefficient (-0.39). Square it (0.1521) and add it to both sides. Add '0.1521' to each side of the equation. -0.78d + 0.1521 + d2 = -0.1521 + 0.1521 Reorder the terms: 0.1521 + -0.78d + d2 = -0.1521 + 0.1521 Combine like terms: -0.1521 + 0.1521 = 0.0000 0.1521 + -0.78d + d2 = 0.0000 Factor a perfect square on the left side: (d + -0.39)(d + -0.39) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (d + -0.39) equal to 0.0000 and 0.0000.Subproblem 1
d + -0.39 = 0.0000 Simplifying d + -0.39 = 0.0000 Reorder the terms: -0.39 + d = 0.0000 Solving -0.39 + d = 0.0000 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.39' to each side of the equation. -0.39 + 0.39 + d = 0.0000 + 0.39 Combine like terms: -0.39 + 0.39 = 0.00 0.00 + d = 0.0000 + 0.39 d = 0.0000 + 0.39 Combine like terms: 0.0000 + 0.39 = 0.39 d = 0.39 Simplifying d = 0.39Subproblem 2
d + -0.39 = 0.0000 Simplifying d + -0.39 = 0.0000 Reorder the terms: -0.39 + d = 0.0000 Solving -0.39 + d = 0.0000 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.39' to each side of the equation. -0.39 + 0.39 + d = 0.0000 + 0.39 Combine like terms: -0.39 + 0.39 = 0.00 0.00 + d = 0.0000 + 0.39 d = 0.0000 + 0.39 Combine like terms: 0.0000 + 0.39 = 0.39 d = 0.39 Simplifying d = 0.39Solution
The solution to the problem is based on the solutions from the subproblems. d = {0.39, 0.39}
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