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Simplifying d2 + -3d = 6 Reorder the terms: -3d + d2 = 6 Solving -3d + d2 = 6 Solving for variable 'd'. Reorder the terms: -6 + -3d + d2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -3d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -3d + 6 + d2 = 0 + 6 Reorder the terms: -6 + 6 + -3d + d2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3d + d2 = 0 + 6 -3d + d2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3d + d2 = 6 The d term is -3d. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3d + 2.25 + d2 = 6 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + -3d + d2 = 8.25 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (d + -1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
d + -1.5 = 2.872281323 Simplifying d + -1.5 = 2.872281323 Reorder the terms: -1.5 + d = 2.872281323 Solving -1.5 + d = 2.872281323 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = 2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 2.872281323 + 1.5 d = 2.872281323 + 1.5 Combine like terms: 2.872281323 + 1.5 = 4.372281323 d = 4.372281323 Simplifying d = 4.372281323Subproblem 2
d + -1.5 = -2.872281323 Simplifying d + -1.5 = -2.872281323 Reorder the terms: -1.5 + d = -2.872281323 Solving -1.5 + d = -2.872281323 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + d = -2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -2.872281323 + 1.5 d = -2.872281323 + 1.5 Combine like terms: -2.872281323 + 1.5 = -1.372281323 d = -1.372281323 Simplifying d = -1.372281323Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.372281323, -1.372281323}
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