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Simplifying 3d2 + -9d = 39 Reorder the terms: -9d + 3d2 = 39 Solving -9d + 3d2 = 39 Solving for variable 'd'. Reorder the terms: -39 + -9d + 3d2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + -9d + 3d2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + -3d + d2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -3d + d2)' equal to zero and attempt to solve: Simplifying -13 + -3d + d2 = 0 Solving -13 + -3d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -3d + 13 + d2 = 0 + 13 Reorder the terms: -13 + 13 + -3d + d2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -3d + d2 = 0 + 13 -3d + d2 = 0 + 13 Combine like terms: 0 + 13 = 13 -3d + d2 = 13 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 = 13 + 2.25 Reorder the terms: 2.25 + -3d + d2 = 13 + 2.25 Combine like terms: 13 + 2.25 = 15.25 2.25 + -3d + d2 = 15.25 Factor a perfect square on the left side: (d + -1.5)(d + -1.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (d + -1.5) equal to 3.905124838 and -3.905124838.Subproblem 1
d + -1.5 = 3.905124838 Simplifying d + -1.5 = 3.905124838 Reorder the terms: -1.5 + d = 3.905124838 Solving -1.5 + d = 3.905124838 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 = 3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = 3.905124838 + 1.5 d = 3.905124838 + 1.5 Combine like terms: 3.905124838 + 1.5 = 5.405124838 d = 5.405124838 Simplifying d = 5.405124838Subproblem 2
d + -1.5 = -3.905124838 Simplifying d + -1.5 = -3.905124838 Reorder the terms: -1.5 + d = -3.905124838 Solving -1.5 + d = -3.905124838 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 = -3.905124838 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + d = -3.905124838 + 1.5 d = -3.905124838 + 1.5 Combine like terms: -3.905124838 + 1.5 = -2.405124838 d = -2.405124838 Simplifying d = -2.405124838Solution
The solution to the problem is based on the solutions from the subproblems. d = {5.405124838, -2.405124838}Solution
d = {5.405124838, -2.405124838}
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