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Simplifying 2d2 + 4d + -62 = 0 Reorder the terms: -62 + 4d + 2d2 = 0 Solving -62 + 4d + 2d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + 2d + d2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + 2d + d2)' equal to zero and attempt to solve: Simplifying -31 + 2d + d2 = 0 Solving -31 + 2d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 2d + 31 + d2 = 0 + 31 Reorder the terms: -31 + 31 + 2d + d2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2d + d2 = 0 + 31 2d + d2 = 0 + 31 Combine like terms: 0 + 31 = 31 2d + d2 = 31 The d term is 2d. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2d + 1 + d2 = 31 + 1 Reorder the terms: 1 + 2d + d2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + 2d + d2 = 32 Factor a perfect square on the left side: (d + 1)(d + 1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (d + 1) equal to 5.656854249 and -5.656854249.Subproblem 1
d + 1 = 5.656854249 Simplifying d + 1 = 5.656854249 Reorder the terms: 1 + d = 5.656854249 Solving 1 + d = 5.656854249 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + d = 5.656854249 + -1 d = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 d = 4.656854249 Simplifying d = 4.656854249Subproblem 2
d + 1 = -5.656854249 Simplifying d + 1 = -5.656854249 Reorder the terms: 1 + d = -5.656854249 Solving 1 + d = -5.656854249 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + d = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + d = -5.656854249 + -1 d = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 d = -6.656854249 Simplifying d = -6.656854249Solution
The solution to the problem is based on the solutions from the subproblems. d = {4.656854249, -6.656854249}Solution
d = {4.656854249, -6.656854249}
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