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Simplifying 3d3 + -2d2 = 24d Reorder the terms: -2d2 + 3d3 = 24d Solving -2d2 + 3d3 = 24d Solving for variable 'd'. Reorder the terms: -24d + -2d2 + 3d3 = 24d + -24d Combine like terms: 24d + -24d = 0 -24d + -2d2 + 3d3 = 0 Factor out the Greatest Common Factor (GCF), 'd'. d(-24 + -2d + 3d2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-24 + -2d + 3d2)' equal to zero and attempt to solve: Simplifying -24 + -2d + 3d2 = 0 Solving -24 + -2d + 3d2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -8 + -0.6666666667d + d2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.6666666667d + 8 + d2 = 0 + 8 Reorder the terms: -8 + 8 + -0.6666666667d + d2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.6666666667d + d2 = 0 + 8 -0.6666666667d + d2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.6666666667d + d2 = 8 The d term is -0.6666666667d. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667d + 0.1111111112 + d2 = 8 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667d + d2 = 8 + 0.1111111112 Combine like terms: 8 + 0.1111111112 = 8.1111111112 0.1111111112 + -0.6666666667d + d2 = 8.1111111112 Factor a perfect square on the left side: (d + -0.3333333334)(d + -0.3333333334) = 8.1111111112 Calculate the square root of the right side: 2.848001248 Break this problem into two subproblems by setting (d + -0.3333333334) equal to 2.848001248 and -2.848001248.Subproblem 1
d + -0.3333333334 = 2.848001248 Simplifying d + -0.3333333334 = 2.848001248 Reorder the terms: -0.3333333334 + d = 2.848001248 Solving -0.3333333334 + d = 2.848001248 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + d = 2.848001248 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + d = 2.848001248 + 0.3333333334 d = 2.848001248 + 0.3333333334 Combine like terms: 2.848001248 + 0.3333333334 = 3.1813345814 d = 3.1813345814 Simplifying d = 3.1813345814Subproblem 2
d + -0.3333333334 = -2.848001248 Simplifying d + -0.3333333334 = -2.848001248 Reorder the terms: -0.3333333334 + d = -2.848001248 Solving -0.3333333334 + d = -2.848001248 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + d = -2.848001248 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + d = -2.848001248 + 0.3333333334 d = -2.848001248 + 0.3333333334 Combine like terms: -2.848001248 + 0.3333333334 = -2.5146679146 d = -2.5146679146 Simplifying d = -2.5146679146Solution
The solution to the problem is based on the solutions from the subproblems. d = {3.1813345814, -2.5146679146}Solution
d = {0, 3.1813345814, -2.5146679146}
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