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Simplifying (d + 2)(d + -5) = 6 Reorder the terms: (2 + d)(d + -5) = 6 Reorder the terms: (2 + d)(-5 + d) = 6 Multiply (2 + d) * (-5 + d) (2(-5 + d) + d(-5 + d)) = 6 ((-5 * 2 + d * 2) + d(-5 + d)) = 6 ((-10 + 2d) + d(-5 + d)) = 6 (-10 + 2d + (-5 * d + d * d)) = 6 (-10 + 2d + (-5d + d2)) = 6 Combine like terms: 2d + -5d = -3d (-10 + -3d + d2) = 6 Solving -10 + -3d + d2 = 6 Solving for variable 'd'. Reorder the terms: -10 + -6 + -3d + d2 = 6 + -6 Combine like terms: -10 + -6 = -16 -16 + -3d + d2 = 6 + -6 Combine like terms: 6 + -6 = 0 -16 + -3d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -3d + 16 + d2 = 0 + 16 Reorder the terms: -16 + 16 + -3d + d2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3d + d2 = 0 + 16 -3d + d2 = 0 + 16 Combine like terms: 0 + 16 = 16 -3d + d2 = 16 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 = 16 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 16 + 2.25 Combine like terms: 16 + 2.25 = 18.25 2.25 + -3d + d2 = 18.25 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (d + -1.5) equal to 4.272001873 and -4.272001873.Subproblem 1
d + -1.5 = 4.272001873 Simplifying d + -1.5 = 4.272001873 Reorder the terms: -1.5 + d = 4.272001873 Solving -1.5 + d = 4.272001873 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 = 4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 4.272001873 + 1.5 d = 4.272001873 + 1.5 Combine like terms: 4.272001873 + 1.5 = 5.772001873 d = 5.772001873 Simplifying d = 5.772001873Subproblem 2
d + -1.5 = -4.272001873 Simplifying d + -1.5 = -4.272001873 Reorder the terms: -1.5 + d = -4.272001873 Solving -1.5 + d = -4.272001873 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 = -4.272001873 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -4.272001873 + 1.5 d = -4.272001873 + 1.5 Combine like terms: -4.272001873 + 1.5 = -2.772001873 d = -2.772001873 Simplifying d = -2.772001873Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.772001873, -2.772001873}
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