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Simplifying 5d3 + 3d2 + -10d = 0 Reorder the terms: -10d + 3d2 + 5d3 = 0 Solving -10d + 3d2 + 5d3 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'd'. d(-10 + 3d + 5d2) = 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 '(-10 + 3d + 5d2)' equal to zero and attempt to solve: Simplifying -10 + 3d + 5d2 = 0 Solving -10 + 3d + 5d2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + 0.6d + d2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6d + 2 + d2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6d + d2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6d + d2 = 0 + 2 0.6d + d2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6d + d2 = 2 The d term is 0.6d. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6d + 0.09 + d2 = 2 + 0.09 Reorder the terms: 0.09 + 0.6d + d2 = 2 + 0.09 Combine like terms: 2 + 0.09 = 2.09 0.09 + 0.6d + d2 = 2.09 Factor a perfect square on the left side: (d + 0.3)(d + 0.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (d + 0.3) equal to 1.445683229 and -1.445683229.Subproblem 1
d + 0.3 = 1.445683229 Simplifying d + 0.3 = 1.445683229 Reorder the terms: 0.3 + d = 1.445683229 Solving 0.3 + d = 1.445683229 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + d = 1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + d = 1.445683229 + -0.3 d = 1.445683229 + -0.3 Combine like terms: 1.445683229 + -0.3 = 1.145683229 d = 1.145683229 Simplifying d = 1.145683229Subproblem 2
d + 0.3 = -1.445683229 Simplifying d + 0.3 = -1.445683229 Reorder the terms: 0.3 + d = -1.445683229 Solving 0.3 + d = -1.445683229 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + d = -1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + d = -1.445683229 + -0.3 d = -1.445683229 + -0.3 Combine like terms: -1.445683229 + -0.3 = -1.745683229 d = -1.745683229 Simplifying d = -1.745683229Solution
The solution to the problem is based on the solutions from the subproblems. d = {1.145683229, -1.745683229}Solution
d = {0, 1.145683229, -1.745683229}
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